. Now because the area of a semi-circle is (diameter)^2 , we can find the volume by evaluating
the integral (4)(4 − x^2 ) dx = dx.
We get (4 − x^2 ) dx = .
Here are some solved problems. Do each problem, covering the answer first, then check your answer.
PROBLEM 1. Find the volume of the solid that results when the region bounded by the curve y = 16 − x^2
and the curve y = 16 − 4x is rotated about the x-axis. Use the washer method and set up but do not
evaluate the integral.
Answer: First, sketch the region.
Next, find where the curves intersect by setting the two equations equal to each other.
16 − x^2 = 16 − 4x
x^2 = 4x
x^2 − 4x = 0
x = 0, 4Slicing vertically, the top curve is always y = 16 − x^2 and the bottom is always y = 16 − 4x, so the integral