Chapter 8.3, Problem 48E

The region bounded by the curve y=x²-2 and the lines y=-2 and x=2 is rotated about the line y=-2. Calculate the volume of the solid formed.

Sketch the region R bounded by y = x2 + 3, x-axis, x = 1 and x = 2.Find,(i) the area of the region R.(ii) the volume of the solid obtained by rotating the region R about theline y = 7.

Find the volume of the solid of revolution generated by revolving the region in the first quadrant bounded by the x-axis and the graph of y = 4x – x² about the following. (a) the x-axis (b) the y-axis (c) the line x = 5 (d) the y = 4