1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Equating integrands on two equal integrals?