Our integral for the area isEvaluating the integral, we get
(b) Find the volume of the solid generated when R is revolved about the x-axis.
In order to find the volume of a region between y = f (x) and y = g(x), from x = a to x = b,
when it is revolved around the x-axis, we use the following formula:
Here, our integral for the area is
Evaluating the integral, we get
(c) The section of a certain solid cut by any plane perpendicular to the x-axis is a circle with
the endpoints of its diameter lying on the parabolas y^2 = x and x^2 = y. Find the volume of the
solid.Whenever we want to find the volume of a solid, formed by the region between y = f(x) and y
= g(x), with a known cross-section, from x = a to x = b, when it is revolved around the x-axis,
we use the following formula:
(Note: A(x) is the area of the cross-section.) We find the area of the cross-section by using the