If you slice this region vertically, each cross-section looks like a washer (hence the phrase “washer
method”).
The outer radius is R = x^3 and the inner radius is r = x^2 . To find the area of the region between the two
circles, take the area of the outer circle, πR^2 , and subtract the area of the inner circle, πr^2.
We can simplify this to
πR^2 − πr^2 = π(R^2 − r^2 )Because the outer radius is R = x^3 and the inner radius is r = x^2 , the area of each region is π(x^6 − x^4 ). You
can sum up these regions using the integral.
π (x^6 − x^4 ) dx = Here’s the general idea: In a region whose area is bounded above by the curve y = f(x) and below by the
curve y = g(x), on the interval [a, b], then each washer will have an area of