Question

The base of a solid is a region located in quadrant 1 that is bounded by the axes, the graph of y = x^2 - 1, and the line x = 2. If cross-sections perpendicular to the x-axis are squares, what would be the volume of this solid?

Answer 1

Hmmm. The y-axis does not form part of the boundary.

Each square of thickness dx has a base that is y=x^2-1 in width.

So, adding up all the squares, the volume v is

∫[1,2] (x^2-1)^2 dx = 38/15