77. Noncircular cylinder A solid right (noncircular) cylinder has its base R in the xy-plane and is bounded above by the paraboloid z = x² + y?. The cylinder's volume is r2 c2-y (x² + y²) dx dy + || (x² + y²) dx dy. Sketch the base region R and express the cylinder's volume as a single iterated integral with the order of integration reversed. Then evaluate the integral to find the volume.

A) Find and describe the region inscribed by the lines (x-axis), (y = -x+2) and (x = 2y-4) under the mapping function (w=1/z)

z = 8 – 3(x? + y²), z = (x² + y²)² - 2 The volume of the solid given by the two surfaces is

Given D is the finite region in upper half plane bounded by the line x + y = 1 and the coordinate axis evaluate the double integral (−3 · x - y² - y² + 2 · x²) dady. . (You may find it useful to sketch the region)