The discussion revolves around a problem from "Probability, Random Variables and Stochastic Processes" (4th ed.) by Papoulis, specifically on page 183. The user seeks clarification on how a particular value in the problem was derived, which is marked in a provided PDF. The solution involves calculating the area of a shaded region using double integrals in Cartesian coordinates, expressed as A = ∫∫_S dA = ∫∫_S dx dy. The user questions whether the transformation x = z - y and dx = dz is applicable in this context.
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HallsofIvy said:They are calculating the area of the shaded region. The area of region S, is [itex]A= \int_S\int dA[/itex] which, in Cartesian coordinates, is [itex]\int_S\int dxdy[/itex]. Of course dxdy= 1 dxdy.