1. Jul 12, 2012 #1

   drewfstr314

   

   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!

    

   drewfstr314, Jul 12, 2012
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3. Jul 12, 2012 #2

   lugita15

   

   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.

    

   lugita15, Jul 12, 2012

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