Homework Help: Find the integral x^3 sqrt(x^2 + x^8 + 8) cos x dx

golb0016 · Dec 1, 2009

1. The problem statement, all variables and given/known data
Find the integral

f(x) = x^3 sqrt(x^2 + x^8 + 8) cox(x) dx

3. The attempt at a solution

I need help starting. It appears to be either integration by parts and/or substituion.

Dick · Dec 1, 2009

Re: Integral

You are going to have a tough time finding an antiderivative for that. Is it actually a definite integral?

golb0016 · Dec 1, 2009

Re: Integral

The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?

Dick · Dec 1, 2009

Re: Integral

golb0016 said: ↑

The problem wanted the function evaluated from -14 to 14. Does it make a difference if it is definitive or not? Is there a trick if it is definitive?

It does in this case. For your function f(-x)=(-f(x)), it's an odd function. What happens if you integrate an odd function over a symmetric interval around the origin?

golb0016 · Dec 1, 2009

Re: Integral

Does the positive and negative parts cancel out if it is symmetric?

Dick · Dec 1, 2009

Re: Integral

golb0016 said: ↑

Does the positive and negative parts cancel out if it is symmetric?

That's the idea.