# Double Integrals by Summing Values of a Cumulative Distribution Function

Double Integrals by Summing Values of a Cumulative Distribution Function

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Let be a function, and suppose that its "cumulative distribution function" , is known. is the integral of over the rectangle below and to the left of , and the double integral of over a rectangle can be computed easily in terms of the values of at the corners via:

f

F(x,y)=f(u,v)dudv

y

∫

u=0

x

∫

v=0

F(P)

f

P

f

F

∫∫

ABCD

Checking boxes causes a region to be shaded such that the combination values at the checked corners is the integral of over the shaded region.

F

f