Question

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical dish or washer.

y= 2 - 1/2x, y=0, x=1, x=2 about the x-axis

Answer 1

So you are adding up circle with radius of (2-1/2x)

Answer 2

\[\pi \int\limits _1^2\left(2-\frac{1}{2}x\right)^2 dx\]

Answer 3

\[\pi \int\limits _1^24-2 x+\frac{x^2}{4}dx\]