simple integration problem#2

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January 23rd 2009, 12:33 AM
slaypullingcat

simple integration problem#2

I'm back, how do I integrate (x^2+2)^2? I need to integrate this to find the volume of a solid. Cheers
January 23rd 2009, 12:54 AM
Moo

Hello,

Quote:

Originally Posted by slaypullingcat

I'm back, how do I integrate (x^2+2)^2? I need to integrate this to find the volume of a solid. Cheers

$(x^2+2)^2=x^4+4x^2+4$

I'm sure you can handle it from here :D
January 23rd 2009, 01:11 AM
slaypullingcat

thanks very much. Out of curiosity, is that the normal method of solving a question like that? Expand it then integrate as usual? What happens with higher powers? Is there a rule I should know about?
January 23rd 2009, 01:23 AM
Moo

Quote:

Originally Posted by slaypullingcat

thanks very much. Out of curiosity, is that the normal method of solving a question like that? Expand it then integrate as usual? What happens with higher powers? Is there a rule I should know about?

Well, with higher powers you can use the binomial theorem, but it's likely not to give you a nice form.

Otherwise, see if you can have something in the form $u'(x) [u(x)]^n$ which has the following antiderivative : $\frac{[u(x)]^{n+1}}{n+1}+C$
January 23rd 2009, 01:38 AM
mr fantastic

Quote:

Originally Posted by slaypullingcat

I'm back, how do I integrate (x^2+2)^2? I need to integrate this to find the volume of a solid.

It probably would be better if you posted the whole question and then showed your working up to this stage (just in case this is the wrong integral).
January 23rd 2009, 02:17 AM
slaypullingcat

Thanks a lot for your help. I appreciate you taking the time. Cheers

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