Is there a formula for calculating the product of integrals, something like:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\left(\int_a^b f(x) dx\right) \times \left(\int_c^d g(y) dy\right)[/itex]

when there is no closed-form expression for F(x) and G(y).

Actually, the functions are almost identical,

[itex] f(x) = x^p e^{-x} \text{ and } g(y) = y^q e^{-y}[/itex]

where p, q are algebraic expressions.

[itex] F(x) = -\Gamma(x, p) \text{ and } G(x) = -\Gamma(y, q)[/itex]

and [itex] \Gamma(x, p) [/itex] is defined as another definite integral with an almost identical integrand.

Thus, is there a way to multiply definite integrals (without knowing the antiderivative) to form one (double?) integral?

Thanks

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# Finding the Product of Integrals

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