Chapter 8.3, Problem 64E

To determine

To check : the statement is true or false.

Answer to Problem 64E

The statement is false.

Explanation of Solution

Given information : If the region enclosed by the y-axis, the line $y=2$ , and the curve $y=\sqrt{x}$ is revolved about the y-axis, the volume of the solid is given by the definite integral ${\displaystyle \underset{0}{\overset{2}{\int }}\pi y^{2}dy}$ .

The statement is false.

The volume is given by:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{2}{\int }}\pi {\left(y^2\right)}^{2}dy}\\ {\displaystyle \underset{0}{\overset{2}{\int }}\pi \left(y^4\right)dy}\end{array}$