the x-axis, and the line x = 1. Then find the volume of the solid generated by rotating R around the line x =2.4. Sketch the region R bounded by the x-axis, and the line x = 1. Then find the volume of the solid generated by rotating R around the line x =2.
Solution: The region is below the y = x3 curve, above the x-axis, and to the left of the x = 1 axis.
Using cylindrical shells to calculate the volume, the radius of such a cylinder is 2 - x, and the height is x3. Consequently the integral is
