Quantum Mechanics Integral Trouble

[jakePHYS]

1. Problem: int[(x^2)*(sin^2 (n*Pi*x/a)] from 0 to a

3. Physics teacher tells me to just look it up. I've wrestled with every table of integrals I can find (web, library, my books), but I'm still hung up.

 

[Dick]

Write it as x^2*sin(k*x) where k is n*pi/a. First use the trig identity sin^2(kx)=(1-cos(2kx))/2. Then to integrate something like x^2*cos(2kx) you just have to integrate by parts twice. It's not the easiest integral in the world, but it's not the hardest either.

 

[jakePHYS]

Thnx

This has been vexing me for 3 1/2 weeks now! THANK YOU!

 

[Dick]

If you are allowed to just look things up, you also might want to check out: http://integrals.wolfram.com/index.jsp You're welcome!