# 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