Infinite square well. probability isues.

[OGrowli]

(a) Obtain the ground state wave function and energy. Draw the wave function
$$\psi_{1}(x)$$
(how many nodes are there in the ground state?) and the probability
$$\left | \psi_{1}(x) \right |^{2}$$
of finding the particle in dx about x.

$$V(x)=\begin{cases}<br /> & \infty,\text{ }x \geq a, x\leq -a \\ <br /> & 0,\text{ } -a< x< a <br /> \end{cases}$$

I've found the ground state wave function and energy to be:

$$\psi_{1}(x)=\sqrt{\frac{1}{a}}sin(\frac{\pi}{a}x)$$
$$E_{1}=\frac{\hbar^{2}\pi^{2}}{2m}$$

I'm not quite sure what is meant by "and the probability $$\left | \psi_{1}(x) \right |^{2}$$ of finding the particle in dx about x."

Are they literally asking for $$\left | \psi_{1}(x) \right |^{2}$$or are they looking for an integral such as:
$$\int_{x-dx}^{x+dx}\left | \psi_{1}(x^{'}) \right |^{2}dx^{'}$$

 

[betel]

They are not asking for the integral, (which would be trivial btw), but they want to know the probability of finding the particle around a certain point x in the well.