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## Homework Statement

Determine the probability of finding a particle of mass m between x=0 and x=L/10, if it is in n=3 state of an infinite well.

## Homework Equations

[tex]P = \int_a^b\left |\psi\left(x\right)\right|^2 dx[/tex]

[tex]\left|\psi\right|^2 = \frac{2}{L}Sin^2\left(\frac{nx\pi}{L}\right)[/tex]

## The Attempt at a Solution

I'm trying to integrate...

[tex]\int_0^{\frac{L}{10}}\frac 2 L \sin^{2}\left(\frac{3x\pi}{L}\right)dx[/tex]

step (1)

[tex]\frac{1}{L}\left[ \int_0^\frac{L}{10}1-\int_0^\frac{L}{10}Cos\left(\frac{6x\pi}{L}\right)\right]dx[/tex]step (2)

[tex]\frac{1}{L}\left[\frac{L}{10} - Sin\left(\frac{3\pi}{5}\right)\right] [/tex]

When I finish solving, I end up with an L in the answer...

which I know I'm not suppose to have, did I mess up my integration somewhere?

sorry about my pooooor pooor latex

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