Question

The nose "cone" of a rocket is a paraboloid obtained by revolving the curve y= sqrt(x), 0 <= x <= 5 about the x-axis, where x is measured in feet. Estimate the volume of the cone by partitioning [0,5] into 5 subintervals of equal length, slicing the cone with planes perpendicular to the x-axis at the subintervals left endpoints, constructing cylinders of height 1 based on cross sections at these points finding the volume of these cylinders. Repeat with midpoints of subintervals.