does anyone know calculus here

[Steven1621]

hey i have a rather difficult integration problem that i just cannot solve and i figure that macrumors people are rather smart so i figured i would see if anyone here knew how to do this.

the integration is (3x^(1/2))/(1+x^(3/4)) dx

i really just need the first few steps and i should be able to figure it out from there.

thanks!

[Vlade]

Hehe, I just accidently differentiated it, but I can't figure out how to integrate it. Anyone have a TI89 calculator?

[yoman]

hey i have a rather difficult integration problem that i just cannot solve and i figure that macrumors people are rather smart so i figured i would see if anyone here knew how to do this.

the integration is (3x^(1/2))/(1+x^(3/4)) dx

i really just need the first few steps and i should be able to figure it out from there.

thanks!

try splitting it up like this:

3x^(1/2) * (1+x^(3/4))^-1

then integrate.

[MoparShaha]

Anyone have a TI89 calculator?As a matter of fact, I do :D.

Answer is:

-4(ln(x^(3/4)+1)-x^(3/4))

I haven't actually tried it on paper, but it looks like an integration by parts problem.

[reaper]

Try thinking about the integration in terms of the 3x^(1/2) piece being a component of an initial (1+x^x)^y term. This way, that x^x component will have to in some way (using multipliers) differentiate out into the resultant 3x^(1/2). Also, some cancellations will probably occur to make it all look pretty.

Backwards thinking is always the hardest, and yet, for me, was always the most rewarding. Hope this helps without giving you too much of a hint (i.e., doing the work for you). See where it takes you and don't be afraid to do trial-and-error... sometimes that's the only way with these sorts of problems.

- reaper

[King Cobra]

I think it's substitution.

TIP: The integral sign on a Mac keyboard is: option-b

So, you have:
∫(3x^(1/2))/(1+x^(3/4))dx

--> Let u = x^(3/4)

That means x^(1/2) = u^(2/3)
and x^(1/4) = u^(1/3)

So, for du:

du = 3/(4x^(1/4)) = 3/(4u^(1/3)) du
EDIT: (error spotted by Veldek) it should read: du = 3/(4x^(1/4)) = 3/(4u^(1/3)) dx


When you bring all that back into the integral and simplify, you should have:

∫u/(1+u) du

That is an integration by parts problem.

[reaper]

As a matter of fact, I do :D.

Answer is:

-4(ln(x^(3/4)+1)-x^(3/4))

I haven't actually tried it on paper, but it looks like an integration by parts problem.

Ack... you gave him the answer. Where't the fun in that? :p

- reaper

[legion]

hey i have a rather difficult integration problem that i just cannot solve and i figure that macrumors people are rather smart so i figured i would see if anyone here knew how to do this.

the integration is (3x^(1/2))/(1+x^(3/4)) dx

i really just need the first few steps and i should be able to figure it out from there.

thanks!

Wow, don't feel like doing your homework the right way, huh? :rolleyes: I just realized I looked at 2 posts from you to do calculus homework. When you get to your first year in college and plan to do any more math classes, it won't get easier and it's time to learn all the tricks (substitution, by parts, etc) now. (and memorize the tables of integrals)

I take it from your sig that you're currently a HS senior.

[Steven1621]

Wow, don't feel like doing your homework the right way, huh? :rolleyes: I just realized I looked at 2 posts from you to do calculus homework. When you get to your first year in college and plan to do any more math classes, it won't get easier and it's time to learn all the tricks (substitution, by parts, etc) now. (and memorize the tables of integrals)

I take it from your sig that you're currently a HS senior.

i certainly know my calculus, but there are integrations that simply are rather challenging and i would say this is one of them. and with this being one of the last assignments of my senior year in high school, i would say that i would just like to be done with it.

[Neserk]

Sadly, I skipped Calculus because I was too worried about my GPA :rolleyes: If I had it to do over I say: screw the GPA take Calculus. The even sadder thing is I'm actually very good in math.

[themadchemist]

I think it's substitution.

TIP: The integral sign on a Mac keyboard is: option-b

So, you have:
?(3x^(1/2))/(1+x^(3/4))dx

--> Let u = x^(3/4)

That means x^(1/2) = u^(2/3)
and x^(1/4) = u^(1/3)

So, for du:

du = 3/(4x^(1/4)) = 3/(4u^(1/3)) du


When you bring all that back into the integral and simplify, you should have:

?u/(1+u) du

That is an integration by parts problem.

Actually, there's a careless mistake here of some importance. 3x^(1/2)=3(u-1)^(2/3). I thik that King Cobra forgot about the pesky integer within the power function. Actually, that integer complicates things QUITE a bit. However, bite your lip with repeated integration by parts (if I'm not mistaken, it'll take more than one) and you should be fine.

Keep in mind: Make dv as complicated as you can while still being able to integrate it reasonably. u will generally be the more complicated of the two parts and with good reason: It's easier to differentiate than to integrate.

Good luck!

[Veldek]

It’s substitution, but you don‘t substitute u=x^(3/4), but u=x^(3/2). Then you get

du = 3/2 * x^(1/2) dx.

Now, when you transfer the integral to

2/(1+x^(3/4)) * 3/2 * x^(1/2) dx

you can do the substitution and get

2/(1+u^(1/2)) du

The rest is up to you.

[King Cobra]

Actually, there's a careless mistake here of some importance. 3x^(1/2)=3(u-1)^(2/3). I thik that King Cobra forgot about the pesky integer within the power function.

I don't see that error. I took the substitution: u = x^(3/4) -- for now, focus on that substitution, as I'll get to the recommended substitution in the above post shortly.

Then I rose the power of both sides to the (2/3) power.
u = x^(3/4) becomes
u^(2/3) = x^(2/4), or simply x^(1/2)

Likewise, to get to u^(1/3), I rose the power of both sides of -- u = x^(3/4) -- to the (1/3) power.
u = x^(3/4) becomes
u^(1/3) = x^(1/4) <-- that step is needed to substitite in a "u" of some form into x^(1/4) when finding du.


It’s substitution, but you don‘t substitute u=x^(3/4), but u=x^(3/2). Then you get...

3/(1+u^(1/2)) du

The rest is up to you.

When I performed that substitution (twice to check for errors), the resulting integral became:

∫ 2 /(1+u^(1/2)) du

Usually, if the original integral has a radical, and you can't resolve that using integration by parts, the chain rule, or du/u, then let "u" = the radical.

[Veldek]

When I performed that substitution (twice to check for errors), the resulting integral became:

∫ 2 /(1+u^(1/2)) du

Usually, if the original integral has a radical, and you can't resolve that using integration by parts, the chain rule, or du/u, then let "u" = the radical.

Oops, you’re right. I forgot that du = 3/2 * x^(1/2).

But that doesn’t change much. As you said the resulting integral is

2/(1+u^(1/2)) du

[Veldek]

I don't see that error. I took the substitution: u = x^(3/4) -- for now, focus on that substitution, as I'll get to the recommended substitution in the above post shortly.

Then I rose the power of both sides to the (2/3) power.
u = x^(3/4) becomes
u^(2/3) = x^(2/4), or simply x^(1/2)

Likewise, to get to u^(1/3), I rose the power of both sides of -- u = x^(3/4) -- to the (1/3) power.
u = x^(3/4) becomes
u^(1/3) = x^(1/4) <-- that step is needed to substitite in a "u" of some form into x^(1/4) when finding du.

So far, it has been correct but then you say that

du = 3/(4u^(1/3)) du

This is obviously not true, so it seems you made a mistake there.

[Abstract]

Wow, don't feel like doing your homework the right way, huh? :rolleyes: I just realized I looked at 2 posts from you to do calculus homework. When you get to your first year in college and plan to do any more math classes, it won't get easier and it's time to learn all the tricks (substitution, by parts, etc) now. (and memorize the tables of integrals)

I take it from your sig that you're currently a HS senior.

Its okay, I think. He only asked on how he should start. The fact that we're giving him more is our business, and icing on the cake for him. :)

try splitting it up like this:

3x^(1/2) * (1+x^(3/4))^-1

then integrate.

That's the way I'd start. Then use substitution by parts twice.

[agreenster]

God. It's only been 6 years since high school calculus, and already this looks like greek to me.

I wasnt GREAT in HS, but I scored a 3 on the AP test.

:(

[1macker1]

You can to download MAPLESOFT's Maple program to "check" all your calculus problems. It's not to hard to learn maple. You get a free 30 day trial i think. It's totally worth the time.

[wPod]

You can to download MAPLESOFT's Maple program to "check" all your calculus problems. It's not to hard to learn maple. You get a free 30 day trial i think. It's totally worth the time.

only do that if you are actually going to check your work!!! in middle school i wrote a calculator program to do quadratics for me (like x^2 +4x -2 =0 what is x?) it was really cool and did just about everything including irrational numbers. and to this day in my calc III course in college i still cannot solve such problems! (well now solving such little algebra is only a small small step, but i still get it wrong! or spend way too much time on it :-/ )

as for the original question, the integration by parts looks good!

[Wes]

Hey, I'm doing a bit of calculus at school and this site has proven to be very handy.

http://integrals.wolfram.com

http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&expr=%283x%5E%281/2%29%29/%281%2Bx%5E%283/4%29%29&x=102&y=16

[themadchemist]

Bah! Stop using calculator symbolic integration! Learn to do it by hand!

[Steven1621]

hey everyone thanks for the help. i had an idea of where i was heading, but had trouble getting the first step, which usually is all i need. this was the tenth of ten very difficult integrations i had to sum up our studies in calc II. again, thanks a lot.

[virividox]

i knew calculus but thank god i forgot it

[legion]

hey everyone thanks for the help. i had an idea of where i was heading, but had trouble getting the first step, which usually is all i need. this was the tenth of ten very difficult integrations i had to sum up our studies in calc II. again, thanks a lot.

This is Calc II? What did they teach you in Calc I... just derivatives? This is part of basic integration and should have been covered in your first 3 months of calculus.

It's only been 10years since I left high school, but wow are they going down hill...

[legion]

Hey, I'm doing a bit of calculus at school and this site has proven to be very handy.

http://integrals.wolfram.com

http://integrals.wolfram.com/graphics.cgi?format=StandardForm&FontSize=Medium&expr=%283x%5E%281/2%29%29/%281%2Bx%5E%283/4%29%29&x=102&y=16

No, you aren't doing calculus. Your computer is. You're nothing but an input device... any 2nd grader could be taught to input things into a program to get an answer.

Learn to do this by hand since it isn't complicated. Using programs and calculators to do calculus should be reserved for harder questions (especially those that don't have exact answers) or when you need to graph or interpolate data points into equations.

[legion]

Bah! Stop using calculator symbolic integration! Learn to do it by hand!

Finally, someone with common sense about helping these kids.

[Neserk]

i knew calculus but thank god i forgot it


:p LOL.

What exactly is Calculus (besides a big scary word?) Is it a take off on Algebra or something completely different?

[Veldek]

:p LOL.

What exactly is Calculus (besides a big scary word?) Is it a take off on Algebra or something completely different?

Calculus and Algebra are two different areas of mathematics. Calculus is about the study of limits and the core is differential and integral calculus.

[King Cobra]

This is Calc II? What did they teach you in Calc I... just derivatives?
Calculus 1 (or Calculus A, depending on where you go) covers limits, derivatives, concepts of changes, and a few integral concepts, and takes up one college semester (about 4 or 5 months). Calculus 2, which is mostly integrals, but also involves infinite series, conics, taylor series, and L'Hôpital's Rule.


This is part of basic integration and should have been covered in your first 3 months of calculus
IF you remember your rules of integrals... any basic integrals that you learned in strictly Calc A involve using the reverse of the rules you solved for derivatives (i.e. power rule, polynomials, product rule, etc.). In Calculus B, you learn more advanced techniques to solve integrals, particularly rules for solving integrals that don't need to be applied to solve derivatives. Such rules include: integration by parts, partial fractions, and trig. substitution (everyone's favorite). I think that even on the AP tests for Calc AB (a combination of topics covering all of Calc A and roughly half of Calc B), integration by parts is considered the Calc B section, but in the late 1990s, all integral questions that required parts were moved to the calculator section of the exam, because there were already plenty of forms of integrals you had to know by the time you took the AP test. So the original integral question is a Calc B topic, not Calc A.


It's only been 10years since I left high school...
Ah, that explains it. http://www.thetechpub.com/phpBB2/images/smiles/icon_eek.gif

[sambo.]

you need to know algbra in order to do calculus.

calculus is to do with rates of change (differential) and limits (integral).

i did it years ago for high-skool and failed miserably when i wnet back to uni last year.

thanx isaac newton...........

[King Cobra]

i did it years ago for high-skool and failed miserably when i wnet back to uni last year.
That just further proves that if you take Calc A or Calc B, and if you're not a mad genius at solving derivatives and integrals, then you better take Calc A and Calc B (then, if need be, Calc C) together so you don't forget your rules of derivatives and integration. I did well in AP Calculus AB in H.S. and waited a semester to take Calc B. I was very well-prepared after H.S. to perform derivatives and integrals, but going into Calc B about 5 months ago (AB doesn't cover all of Calc B, so I had to take Calc B) wasn't a very easy transition. The first week (or 2) in Calc B, I re-learned how to find the volume of a curve revolving around an axis, and it took me a day or so to get back into, specifically, if it's x•(something) or (4-x)•(something) for various volumes.

Also, if you plan to take Calculus C (which I am now as a summer course), then do so no more than 3 months after you take Calc B, because the first half of Calc C involves a lot of what you learned about derivatives and limits from the first half of Calc A, and you already spent Calc B working a lot with more derivatives and integrals.


thanx isaac newton...........
You can also send your regards to L'Hôpital for making some of your limits easier to solve. http://www.thetechpub.com/phpBB2/images/smiles/icon_twisted.gif

[Wes]

No, you aren't doing calculus. Your computer is. You're nothing but an input device... any 2nd grader could be taught to input things into a program to get an answer.

Learn to do this by hand since it isn't complicated. Using programs and calculators to do calculus should be reserved for harder questions (especially those that don't have exact answers) or when you need to graph or interpolate data points into equations.

No sh**, but when you've been trying to do a question for an hour and you keep getting different answers it's nice to know which one is correct. I think I get about 1 point for the answer and between 5 and 10 for the working.

Don't you think the teacher would know if you have a nice long integration by substitution question and then an answer on the next line. :rolleyes: :rolleyes:

[Veldek]

thanx isaac newton...........

Don't forget Leibniz!

[virividox]

:p LOL.

What exactly is Calculus (besides a big scary word?) Is it a take off on Algebra or something completely different?

ill tell you the difference

Algebra is logic and pretty straight forward

Calculus is algebra backwords; it is the anti-thesis to logic and straight forwardness

hehe

in all honesty the only reason i took calc was because i was too proud to go to the standard math class; i dont even do math in university, i guess i just wanted to see if i could do it; which i could, but i decided i dont want to do it any longer :)

[themadchemist]

calculus is to do with rates of change (differential) and limits (integral).


Actually, limits are not "limited" to integrals. The derivative, or rate of change, is a special sort of limit, itself.

Thus, the one unifying concept of calculus is the limit. Other than that, it is a broad, green field, in which one can stoke the flame of his/her cognition.

Those of you who found the two puns in the sentence above, consider yourselves nerds!

BTW, as far as Leibniz, his version was filled with a lot more errors than that of Mr. Newton.

virividox: Calculus, though not always straightforward, is extremely logical. It is governed by the same rigorous requirements of proofs that other branches of mathematics must follow. Moreover, mathematical forms based on calculus explain much of the physical universe. Therefore, calculus is quite logical and is really necessary to actually understanding physical phenomena.

If, however, you blindly apply rules, then Calculus will seem illogical. Think about what you're doing, conceptually. Read the proofs provided in your book. Try to work them out or at least see why they make sense. Then, Calculus will make sense to you.

[King Cobra]

Those of you who found the two puns...consider yourselves nerds!

Luckily I only got one of them. http://www.thetechpub.com/phpBB2/images/smiles/icon_eek.gif http://www.thetechpub.com/phpBB2/images/smiles/icon_biggrin.gif

[Veldek]

BTW, as far as Leibniz, his version was filled with a lot more errors than that of Mr. Newton.

Maybe, but the work of Leibniz has been much better than the work of Newton in other areas, e.g. his use of the d in opposition to the dot. This alone made the Continental European Mathematics surpass English Mathematics until Cambridge started "to introduce the principles of pure d-ism in opposition to the dot-age of the University".

And there's a pun in this, too...

[themadchemist]

Maybe, but the work of Leibniz has been much better than the work of Newton in other areas, e.g. his use of the d in opposition to the dot. This alone made the Continental European Mathematics surpass English Mathematics until Cambridge started "to introduce the principles of pure d-ism in opposition to the dot-age of the University".

And there's a pun in this, too...

Haha, fair enough. I am in favor of d, after all...And delta, too, when it comes to partials.

Great pun, by the way! Is that yours?

[Veldek]

Great pun, by the way! Is that yours?

No, not at all, it's by the Cambridge University.

[themadchemist]

No, not at all, it's by the Cambridge University.

oh, really? Glad to see Cambridge doesn't take itself *too* seriously.

[Steven1621]

This is Calc II? What did they teach you in Calc I... just derivatives? This is part of basic integration and should have been covered in your first 3 months of calculus.

It's only been 10years since I left high school, but wow are they going down hill...

my high school calc class follows the sylabus of the university of connecticut. calc I is sem I and calc II is sem II. integration is covered during sem II

[Steven1621]

Bah! Stop using calculator symbolic integration! Learn to do it by hand!

thats exactly what i need to do. the calculator is useless to me since i have to show all steps anyway. i just need a bit of guidence as to where i should start.

[sambo.]

are we differentiating or integrating some of these appalling puns? i am a nerd it seems, even tho i failed Math181 at uni of wollongong last year.

it was tough trying to re-learn my whole HSC 4-unit math syllabus in a week (needless to say i didn't), but i really should have dropped it before that nasty F found it's way onto my academic record. on day i might actually finish that damn degree, but life keeps getting in the way.......

i agree however; that there is no point in just knowing what buttons on the calculator/'puter to push. much better to know how to do it with good old pencil and paper. if your methodical, and know the rules for integation/differentiation, it's pretty quick to do by hand.

btw - the original Q is an Integration by Parts problem (which has been pointed out several times already), don't ask me the formula, someone else has already posted it (i think....)
;)

[russed]

i chose to do further maths for a level (for some stupid reason) and no matter how hard the calculus got i still found it quite fun, the starting at a problem for like 2 hours and doing about 10 pages of working, stil to get it wrong!

does that make me a geek?

[Doctor Q]

does that make me a geek?Yes, and you should be proud of it and enjoy it!

I've always been a math geek and I don't mind the title at all.

[themadchemist]

thats exactly what i need to do. the calculator is useless to me since i have to show all steps anyway. i just need a bit of guidence as to where i should start.

Fair enough. I'm glad you came to us with your question. I hope the ensuing discussion has been of use.

[russed]

Yes, and you should be proud of it and enjoy it!


YEH! i'm a geek! bring it on!

[agreenster]

I graduated H.S. in 1998 with an A+ in AP Calc 2, and scored either a 3 or 4 (I posted 3 earlier, but for the life of me cant remember) on the AP test.

Okay. After reading everyone's posts, I have little waves of remembrance about Calc, especially when hearing the terms derivatives, power rule, polynomials, product rule, integration by parts, partial fractions, and trig. substitution...

But that's it! Everything else I totally forget! I couldnt solve for x if my life depended on it! How the hell is that possible? I mean, I tested out of most of my math in college (art major) so I can see that I would be rusty, but a TOTAL loss of memory about that subject? I even forget how to solve a derivative for christ's sakes!

Maybe the brain eventually deletes the unused data and replaces it with current stuff. I mean, I'm a computer animator, so I'm constantly challenged with new problems to solve, but when it comes to calc now, I have absolutely no ability.

Makes me want to go back and learn it again, only to prove to myself that I could.

Now THATS geeky.

[themadchemist]

Luckily I only got one of them. http://www.thetechpub.com/phpBB2/images/smiles/icon_eek.gif http://www.thetechpub.com/phpBB2/images/smiles/icon_biggrin.gif

which one?! :D

[King Cobra]

I thought one of the puns had to do with the word "cognition" and having some similarity with "conjugates," but after rereading the sentence, that can't be. So then I'm even less nerdy than I originally suggested.

[themadchemist]

I thought one of the puns had to do with the word "cognition" and having some similarity with "conjugates," but after rereading the sentence, that can't be. So then I'm even less nerdy than I originally suggested.

Yeah, sorry man. For your benefit, and that of everyone else, I shall reveal the punnage.

I said (emphasis added):


Thus, the one unifying concept of calculus is the limit. Other than that, it is a broad, green field, in which one can stoke the flame of his/her cognition


Green's Theorem and Stokes' Theorem are fundamental to multivariable integration. Yay for puns! :D