normalization of time independent wave function

[Skullmonkee]

1. The problem statement, all variables and given/known data
normalize the wave function \Psi(x)= Acos(\Pi*x/a) to show that A=\sqrt{2/a}

3. The attempt at a solution
i dont know how to get that answer as all i can tell, normalizing gives:
-A^{2}pi^{2}2x/a^{2} * sin (pix/a)

However this does not give the right answer for A
Any help pointing out what ive missed would be great.

[xepma]

Hi Skullmonkee,

Let me ask you a question first:

What expression "defines" the normalization of a wavefunction?

[Skullmonkee]

Do you mean this?

\int\Psi^{*}\Psi dx=1

\int Acos(\pi x/a)*Acos(\pi x/a)dx

= \int A^{2}cos^{2}(\pi x/a)

But im not sure where to go from here?

[Redbelly98]

What are the limits of integration? I.e., over what range of x is the wavefunction defined?

[Matterwave]

You need to plug in the limits of integration. You can't normalize a wave function using indefinite integration.