Question

The base of a solid is the region enclosed by y = e^x, the x-axis, the y-axis, and the

line x = 8. Cross sections perpendicular to the x-axis are squares. Find the volume of
the solid.

Answer 1

You can use the definite integral to find the volume of a solid with specific cross sections on an interval, provided you know a formula for the region determined by each cross section. If the cross sections generated are perpendicular to the x‐axis, then their areas will be functions of x, denoted by A(x). The volume ( V) of the solid on the interval [ a, b] is