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

Find the volume under the surface z = f(x,y) and above the rectangle with the given boundaries.z = x2 + y2; 0 ≤ x ≤ 1, 0 ≤ y ≤ 1

Evaluate the double integral over the given region. R = {(x, y): 0 ≤ x ≤ π, 0 ≤ y ≤ 1}

Find the average value of over the given region. + z2 over the rectangular solid in the first octant bounded by the coordinate planes and the planes , ,

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

Find the volume by using polar coordinates.The region bounded by the paraboloid , the cylinder , and the

Find the volume of the indicated region.the region that lies under the plane and over the triangle with vertices at , , and

Find the transformation from the uv plane to the xy plane.u = x + 3y, v = x – 3y

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

Find the Jacobian using the given equations.