(837, # 13) Evaluate the integral

where R = [0,1] x [0,1].

Solution: For each fixed x the corresponding cross section of the solid is a rectangle surmounted by a triangle. The area of the rectangle is 2, the area of the triangle is 1, the area of the cross-section is 3. Since the volume is 1 unit thick along the y-axis, the total volume is 3.

by:rjm