Finding the probability to find a particle in a well

[Vitani11]

Homework Statement

A particle is in the n = 1 state of an infinite square well of size L. T. What is the probability to find the particle in the region Δx = 0.007L at the point x = L/2? 3L/4? (Since Δx is small you don't need to do any integration)

Homework Equations

ψ = Δxf(x)
Δx = 0.007L
f(x) = sin²(nπx/L)

The Attempt at a Solution

I don't understand what I'm doing wrong. I can do the integral but I can't do this without doing the integral. I plugged in L/2 for Δx and x = L/2 for f(x) = sin²(nπx/L). This gave me the correct answer for L/2. But now I am trying to do 3L/4 and when I use the same method I get the wrong answer. I know the RIGHT answer is 0.007 for 3L/4 because of the nature of sine and a drawing of the wave-function in the well. I need to know how to properly do this mathematically- what am I doing wrong here?

 

[TSny]

Can you show more detail of your work for x = 3L/4? Make sure that you are using the normalized wavefunction for the ground state.

 

[Vitani11]

I've figured it out - thank you