1 1. Evaluate // Tr2 + 12)n/2dA, where n is an integer and D is the...

 

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1 1. Evaluate // Tr2 + 12)n/2dA, where n is an integer and D is the region bounded by the circles with the origin as center and radii a and b with 0< a < b. For what values of n does this integral have a limit as a → 0+? 2. Find the area of the region enclosed by the curves rxy = a, xy = b, xy14 = c and xyl4 = d, where 0 < a < b and 0 <c < d, and x > 0, y > 0, by applying the transformation u = xy, v = xyl4 and doing integration over an appropriate region in the uv-plane. 3. Find the volume of the solid common to the spheres p 2/2 cos o and p 2, by doing integration using spherical coordinates. 4. Find the volume of the region R lying below the plane z 3- 2y and above the paraboloid z = x²+ y?. %3D 1 1. Evaluate // Tr2 + 12)n/2dA, where n is an integer and D is the region bounded by the circles with the origin as center and radii a and b with 0< a < b. For what values of n does this integral have a limit as a → 0+? 2. Find the area of the region enclosed by the curves rxy = a, xy = b, xy14 = c and xyl4 = d, where 0 < a < b and 0 <c < d, and x > 0, y > 0, by applying the transformation u = xy, v = xyl4 and doing integration over an appropriate region in the uv-plane. 3. Find the volume of the solid common to the spheres p 2/2 cos o and p 2, by doing integration using spherical coordinates. 4. Find the volume of the region R lying below the plane z 3- 2y and above the paraboloid z = x²+ y?. %3D

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