Integral of a product of three functions?

1. Aug 25, 2009

Diode

Hello there,

I've been battling through my books and searching the web, but nothing seems to give me any ideas on how to tackle this beast bellow:

$$\int_{-\pi }^{\pi } e^{-x^{2}} \sqrt{x^{4}+1} sin x dx$$

This is a reasonably desperate call for any information or literature anyone might know of. If you know of anywhere with material on this or even which techniques I should be looking into it'd be much appreciated!

Thanks,
D =]

2. Aug 25, 2009

VietDao29

Big hint of the day, when encountering these type of definite integrals with the limit from -a to a, one should immediately check to see if the given function is even, or odd.

Can you go from here? :)

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EDIT: Oh, and btw, this thread shouldn't belong to Introductory Physics board.. =.="

3. Aug 25, 2009

Diode

Uh.. is it odd? *crosses fingers* so it's zero?

You might have guessed I'm new here, where should this question go?

4. Aug 25, 2009

rock.freak667

for an odd function f(-x)=-f(x) and an even function f(-x)=f(x)

Calculus & Beyond forum

5. Aug 25, 2009

VietDao29

Yes, it is. It's 0.

Let f(x) be a continuous function on the interval (-a, a).

If f(x) is odd then:

$$\int_{-a} ^ a f(x) = 0$$

And if f(x) is even then:

$$\int_{-a} ^ a f(x) = 2 \int_0 ^ a f(x)$$

You can use a simple u-substitution to prove both of them. Pretty easy, just give it a try if you want. :)

6. Aug 26, 2009

Diode

Thank you both very much! You have saved me a lot of misguided scribbling =]

7. Aug 26, 2009

ideasrule

By the way, there's no indefinite integral for that function:

http://integrals.wolfram.com/index.jsp?expr=%28e^-x^2%29*sqrt%28x^4%2B1%29*sin%28x%29&random=false

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