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Find the Jacobian J(u, v). u = 5x – 3y,      v = -3x + 5y

Use the given transformation to evaluate the integral.

Solve the problem.Let R ={(x, y): 1 ≤ x < 4, 0 ≤ y < 4}. Evaluate  

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.The curve y = ln x and the lines x = 8 and y = 0

Find the transformation from the uv-plane to the xy-plane.,    

Solve the problem.Let R ={(x, y): 1 ≤ x < 5, 0 ≤ y < 7}. Evaluate

Find the average value of F(x, y, z) over the given region.F(x, y, z) = xyz over the rectangular solid in the first octant bounded by the coordinate planes and the planes x = 6, y = 4, z = 3. 

Find the average value of the function f over the given region.; R = {(x, y): 1 ≤ x ≤ 5, 1 ≤ y ≤ 5}

Find the average value of the function f over the given region.; R = {(x, y): 1 ≤ x ≤ 2, 1 ≤ y ≤ 2}

Find the volume by using polar coordinates.The region bounded by the paraboloid z = x2 + y2, the cylinder x2 + y2 = 25, and the xy-plane.