Question

Question #219cb

Answer 1

Please see below.

Explanation:

The equation is equivalent to `y=-1/2x+1`

Because the revolution is about the `x`-axis, the radius of the disk is `r=y=-1/2x+1`.

Because the region is bounded by the axes, `x` varies from `0` to the `x`-intercept at `2`.

So the Volume of the solid is given by

`int_0^2 pi(-1/2x+1)^2 dx = pi/4 int_0^2 (x-2)^2 dx = (2pi)/3`