- #1
drewfstr314
- 20
- 0
Is there a formula for calculating the product of integrals, something like:
[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
[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