A question on integrals

1. Feb 2, 2009

ManyNames

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

So, this is really a question. Suppose you have:

$$a(t)=\int_{\Omega} |\psi|^2$$

and then you have,

$$\frac{\partial t}{\int_{t_0}^{t_1} dt a(t)}$$

Surely this can't be right, because that would imply by substitution

$$\frac{\partial t}{\int_{t_0}^{t_1} dt \int_{\Omega} |\psi|^2}$$

Is that really allowed?

2. Feb 3, 2009

ManyNames

Can no one answer this for me?

3. Feb 3, 2009

chrisk

What is the differential of the integral in the first equation?