Equating integrands on two equal integrals?

[russdot]

Homework Statement

This is more of a general question. If I have two different integrals that equal the same value, is it valid to equate the integrands?

Homework Equations

\int P(\theta,\phi)d\Omega = N
\int Q(\theta',\phi')d\Omega' = N
Where N is a constant and d\Omega = sin\theta d\theta d\phi

The Attempt at a Solution

Since it can be said:
\int Q(\theta',\phi')d\Omega' = N = \int P(\theta,\phi)d\Omega

Is it valid to conclude that
Q(\theta',\phi')d\Omega' = N = P(\theta,\phi)d\Omega ?

Thank you.

 

[Dick]

The integral from 0 to 1 of f(t)=t dt is 1/2. The integral from 0 to 1 of f(t)=(1/2) dt is also 1/2. No, you can't equate the integrands.