π[f(x)^2 − g(x)^2 ]To find the volume, evaluate the integral.
π [f(x)^2 − g(x)^2 ] dxThis is the formula for finding the volume using washers when the region is rotated around the x-axis.
Example 2: Find the volume of the solid that results when the region bounded by y = x and y = x^2 , from x
= 0 to x = 1, is revolved about the x-axis.
Sketch it first.
The top curve is y = x and the bottom curve is y = x^2 throughout the region. Then our formula tells us that
we evaluate the integral.
π (x^2 − x^4 ) dxThe result is
π (x^2 − x^4 ) dx = π =