How do i show this integral equals zero? (I'm quite positive it does)

[PsychonautQQ]

Homework Statement

So on my first day of intro to quantum physics my teacher assigned a lot of calculus problems as homework. One of them problems was a quite lengthy proof that one integral is the equivalent of another, and I am so close to getting the correct answer!

All I need to do to finish my proof is to show that the integral

integral: ((sin(ax)sin(bx))/x) dx between -inf and inf is equal to zero.
I'm having trouble doing this.. help?
I've tried using the trig identity to turn sin(ax)sin(bx) into 1/2(cos(ax-bx) + cos(ax+bx)) but still feel the integral is above my capabilities.. I'm not suppose to use wolfram alpha or such things.

Homework Equations

The Attempt at a Solution

 

[Dick]

Homework Statement

So on my first day of intro to quantum physics my teacher assigned a lot of calculus problems as homework. One of them problems was a quite lengthy proof that one integral is the equivalent of another, and I am so close to getting the correct answer!

All I need to do to finish my proof is to show that the integral

integral: ((sin(ax)sin(bx))/x) dx between -inf and inf is equal to zero.
I'm having trouble doing this.. help?
I've tried using the trig identity to turn sin(ax)sin(bx) into 1/2(cos(ax-bx) + cos(ax+bx)) but still feel the integral is above my capabilities.. I'm not suppose to use wolfram alpha or such things.

Homework Equations

The Attempt at a Solution

Use the symmetry of the integrand. What happens if you replace x with -x?

 

[jedishrfu]

If you were to plot it and then visually inspect it you'd see whether you were right about it being zero then following Dick's advice yo'd be able to prove it.

 

[PsychonautQQ]

ahh it's an odd function! I kept thinking it's an even function but completely forgot to include the x on bottom! Thanks you guys are f'n smart!