Use the given transformation to evaluate the integral.

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

Find the average value of F(x, y, z) over the given region.F(x, y, z) = x9y10z2 over the rectangular solid in the first octant bounded by the coordinate planes and the planes x = 2, y = 1, z = 3.

Use cylindrical coordinates to find the volume of the indicated region.the region enclosed by the paraboloids z = x2 + y2 – 9 and z = 153 – x2 – y2.

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

Find the volume by using polar coordinates.The region bounded by the paraboloid z = x2 + y2, the cylinder x2 + y2 = 49, and the xy-plane.

Use cylindrical coordinates to find the volume of the indicated region.the region enclosed by the paraboloids z = x2 + y2 – 9 and z = 63 – x2 – y2.  

Find the volume by using polar coordinates.The region bounded by the paraboloid z = x2 + y2 ,  the cylinder x2 + y2 = 64, and the xy-plane.

Solve the problem.Let R ={(x, y): 1 ≤ x < 5, 0 ≤ y < 6}. Evaluate  

Evaluate the double integral over the given region.