(first post here 
)
Being R a rectangle [a,b] x [c,d]
Knowing the following:
. . . . .\(\displaystyle f(x,\, y)\, =\, \varphi(x)\, \psi(y)\)
...how do I prove the following?
. . . . .\(\displaystyle \displaystyle \int \int_R\, f(x,\, y)\, dx\, dy\, =\, \left(\int_a^b\, \varphi(x)\, dx\right)\, \left(\int_c^d\, \psi(y)\, dy\right)\)
)Being R a rectangle [a,b] x [c,d]
Knowing the following:
. . . . .\(\displaystyle f(x,\, y)\, =\, \varphi(x)\, \psi(y)\)
...how do I prove the following?
. . . . .\(\displaystyle \displaystyle \int \int_R\, f(x,\, y)\, dx\, dy\, =\, \left(\int_a^b\, \varphi(x)\, dx\right)\, \left(\int_c^d\, \psi(y)\, dy\right)\)
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