Problems

01

Volume of solid of revolution

Consider the region bounded by the curves $y=x$ and $y=x^2$. This region is revolved around each of the axes below. For each axis, set up the integral (do not integrate) giving the volume of the solid of revolution.

• (a) The $x$-axis.
• (b) The $y$-axis.
• (c) The line $y=2$.
• (d) The line $x=1$.

For each axis, include a sketch of the region and an example of disk or washer.

02

Volume of solid of revolution

Consider the region bounded by the curves $y=x$ and $y=4x-x^2$. This region is revolved around each of the axes below. For each axis, set up the integral (do not integrate) giving the volume of the solid of revolution.

• (a) The $x$-axis.
• (b) The line $y=4$.

For each axis, include a sketch of the region and an example of disk or washer.