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**1. Homework Statement**

Calculate the expectation values of x, [tex]x^2[/tex] for a particle in a one dimensional box in state [tex]\Psi_n[/tex]

**2. Homework Equations**

[tex]\Psi_n = \sqrt{\frac{2}{a}}sin(\frac{n\pi x}{a})[/tex]

**3. The Attempt at a Solution**

i formed the integral

[tex]\int_{-\infty}^{+\infty}\Psi ^2 x dx[/tex] as the expectation value of x. (Psi squared simply because this psi is not complex)

this gives [tex]<x>=\frac{2}{a} \int_{-\infty}^{+\infty}x sin^2(\frac{n\pi x}{a})dx[/tex]. The problem is i do not know a way to simplify this integral, similarly i have the problem when there is an x^2 in the integral.

any help would be appreciated