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Equating integrands on two equal integrals?

  1. Oct 17, 2009 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations
    [tex]\int P(\theta,\phi)d\Omega = N[/tex]
    [tex]\int Q(\theta',\phi')d\Omega' = N[/tex]
    Where [tex]N[/tex] is a constant and [tex]d\Omega = sin\theta d\theta d\phi[/tex]

    3. The attempt at a solution
    Since it can be said:
    [tex]\int Q(\theta',\phi')d\Omega' = N = \int P(\theta,\phi)d\Omega[/tex]

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

    Thank you.
  2. jcsd
  3. Oct 17, 2009 #2


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    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.
    Last edited: Oct 17, 2009
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