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.