Question

The base of a solid is the region bounded by y=x2−8 and y=−7. Find the volume of the solid given that the cross sections perpendicular to the x-axis are squares.

Answer 1

To find the volume of the solid, you need to integrate the area of square cross sections across the range defined by the base of the solid.

Step-by-step explanation:

The student asked about finding the volume of a solid with a base bounded by y = x2 − 8 and y = −7, with squares as cross sections perpendicular to the x-axis. To solve this problem, we should integrate the area of these square cross sections across the range where the two equations define the base of the solid. This requires identifying the points of intersection between the curves to set the limits of integration.