Dividing Definite Integrals

  • #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!
 

Answers and Replies

  • #2
1,554
15
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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