Evaluate integral_0^1/16 integral_y^1/4 ^1/2 cos(16 pi x^5)dx dy find the surface area of the sphere x^2 + y^2 + z^2 = 16 inside cylinder x^2 + y^2 = 4y (use the polar coordinate) find the volume of the solid of the cylinder x^2+ y^2 = 16 between the planes z = 1 and x + z = 5 find the volume of the solid that lies in the cone z = squareroot 3x^2+ 3y^2 and below the sphere x^2 + y^2 + z^2 = 4 (use the spherical coordinate) evaluate integral_r (2x^2 + y^2)da where r is the region in the 1^st quadrant bounded by xy = 1, xy = 4, y = 2x, y = 1/2x using x = u and y = v/u assume u > 0 and v > 0