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Integrate x^2 sin(x^2) dx

  • Thread starter jacy
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  • #1
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Hi ,
I am having trouble integrating this problem.

Integrate x^2 sin(x^2) dx

Here is what i did. I used the substitution method.

u = x^2 sqrt u = x
du = 2x dx
du/2x = dx

du/2 sqrt u = dx since sqrt u = x

substituting this in the equation

u sin(u) du/2 sqrt u

Now i don't know how to integrate this. Please help, thanks.
 

Answers and Replies

  • #2
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jacy said:
Hi ,
I am having trouble integrating this problem.

Integrate x^2 sin(x^2) dx
I don't think the antiderivative of your integrand is an elementary....but I don't really know for sure.
 
  • #3
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I believe you're correct. My computer cannot calculate it.
 
  • #4
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apmcavoy said:
I believe you're correct. My computer cannot calculate it.

Thanks 4 ur time. Do u think that problem is wrong.
 
  • #5
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jacy said:
Thanks 4 ur time. Do u think that problem is wrong.
The problem is fine....it's just that you cannot find an elementary antiderivative as a solution.
 
  • #6
GCT
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where'd you obtain the problem?
 
  • #7
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It would work if the integrand was [itex]x\sin{x^{2}}[/itex].
 
  • #8
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GCT said:
where'd you obtain the problem?
Thanks for looking at the problem. My teacher gave this problem on the exam. How can we solve this.
 
  • #9
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Integration by parts might be possible, but my computer and my TI 89 cannot compute it, so there's probably not a simple antiderivative. And you were given this problem on a test? :bugeye:
 
  • #10
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Tony11235 said:
Integration by parts might be possible, but my computer and my TI 89 cannot compute it, so there's probably not a simple antiderivative. And you were given this problem on a test? :bugeye:
Thanks, do u think the substitution method that i used will work. This wasn't the only one there were 3 more.
 
Last edited:
  • #11
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Are you sure it wasn't asking you to evaluate it as a definite integral numerically? That's the only way I can see doing this.
 
  • #12
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apmcavoy said:
Are you sure it wasn't asking you to evaluate it as a definite integral numerically? That's the only way I can see doing this.
No it isn't a definite integral. It's tough one. Hopefully the teacher should provide the solution today. If he does, then can i post the solution in here, thanks.
 
  • #13
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[itex] \int x^2\sin(x^2) dx [/tex]

[itex] \int x^2\sin(x^2) dx = \frac{-x}{2}\cos(x^2) + \frac{1}{2} \int \cos(x^2) dx [/tex]
 
  • #14
Tom Mattson
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whozum said:
[itex] \int x^2\sin(x^2) dx [/tex]

[itex] \int x^2\sin(x^2) dx = \frac{-x}{2}\cos(x^2) + \frac{1}{2} \int \cos(x^2) dx [/tex]
True, but now what's [itex]\frac{1}{2} \int \cos(x^2) dx[/itex]?

jacy, the initial response you received was correct. Your integrand doesn't have an elementary antiderivative. 10 bucks says that the problem was supposed to be [itex]\int x\sin(x^2) dx[/itex].
 
  • #15
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Tom Mattson said:
True, but now what's [itex]\frac{1}{2} \int \cos(x^2) dx[/itex]?

jacy, the initial response you received was correct. Your integrand doesn't have an elementary antiderivative. 10 bucks says that the problem was supposed to be [itex]\int x\sin(x^2) dx[/itex].
Its not elementary i was just trying it out and seeing how far I could get, but figured I'd just post it anyway.
 
  • #16
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Here's the answer from Mathematica in case anyone was wondering. I agree, it was probably supposed to be [tex]\int x\sin{(x^2)}dx[/tex].
 

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  • #17
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Tom Mattson said:
True, but now what's [itex]\frac{1}{2} \int \cos(x^2) dx[/itex]?

jacy, the initial response you received was correct. Your integrand doesn't have an elementary antiderivative. 10 bucks says that the problem was supposed to be [itex]\int x\sin(x^2) dx[/itex].
I don't think so it was a typo. This problem was on the exam, thanks.
 
  • #18
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jacy said:
I don't think so it was a typo. This problem was on the exam, thanks.
Was the problem asking to find the derivative of that function?
 
  • #19
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whozum said:
Was the problem asking to find the derivative of that function?
We have to find the anti derivative of that function. Today the teacher said that he made a typo it should be
integrate x^2 sin^2(x) instead of x^2 sin(x^2)

How did u guys type the sign of integral
 
  • #20
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[tex] \int {x^2 \sin ^2 x\,dx} [/tex]
can be evaluated via integration by parts.

jacy, the integral sign is just \int when using LaTeX.
Try clicking on this integral sign: [tex] \int [/tex]
 
  • #21
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bomba923 said:
[tex] \int {x^2 \sin ^2 x\,dx} [/tex]
can be evaluated via integration by parts.

jacy, the integral sign is just \int when using LaTeX.
Try clicking on this integral sign: [tex] \int [/tex]
Thanks, yea now i can solve it
 

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