Let f(x, y) = e-(x+y) for x ≥ 0 and y ≥ 0. (a) Compute of f(x, y) dx dy (b) Compute the double integral of f(x, y) over the region x ≥ 0 and y ≥ x + 5.
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- You are rotating the region bounded by y 2 = x, y = 1, and x = 0 about the line x = 1. Set up the definite integral using the washer method.Use Green's Theorem to evaluate the line integral of C to the function (y − x) dx + (2x − y) dy for the given path.C: boundary of the region lying between the graphs of y = x and y = x2 − 8xEvaluate the triple integral, 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the plane x = 5.