Write a double integral in Cartesian coordinates that gives the volume of the region in the first octant bounded by the planes +/+= 1 and+/- (z − 1) = 1. You do not need to evaluate the integral.

Find the volume inside x² + y² = 1 and x² + z² = 1.

Consider the region bounded by x = 3y and x = y^2. A solid is formed by rotating the region about the line y = 3. Setup the integral that gives the volume of solid in terms of shells.  You do not have to evaluate the integral

Write a definite integral for the area of the region bounded by y = 2 - x² and y = x². Do not integrate.