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Dividing Definite Integrals

  1. Jul 12, 2012 #1
    Is there a general algebraic way to write the quotient of two definite integrals as one? I mean, what would be

    [itex]\frac{\int_a^b f(s) ds}{\int_c^d g(t) dt}[/itex]

    Is it analogous to the product of integrals creating a double integral?

    Thanks in advance!
  2. jcsd
  3. Jul 12, 2012 #2
    Let's see how a double integral of a product (of functions of different variables) can be written as a product of single integrals:[itex]\int^{d}_{c}\int^{b}_{a}f(s)g(t) dsdt = \int^{d}_{c}g(t)\left(\int^{b}_{a}f(s) ds\right) dt = \left(\int^{b}_{a}f(s) ds\right)\left(\int^{d}_{c}g(t) dt\right)[/itex]. You can verify that the same kind of thing doesn't work for quotients, because the integral of a reciprocal is not the reciprocal of the integral.
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