Chapter 11.3, Problem 62E

To determine

To determine: Whether the statement is true or false.

Answer to Problem 62E

The given statement is false.

Explanation of Solution

Given information:

The statement:

The total area enclosed by the 3-petaled rose $r=3\sin \theta$ is ${\displaystyle \underset{0}{\overset{2\pi }{\int }}\frac{1}{2}{\sin }^{2}3\theta d\theta }$ .

Calculation:

It is known that the integration from 0 to $2\pi$ takes the curve two times. This means that the area of the integration becomes twice. Also, the correct limit of integration should be $\pi$ .

Hence, the given statement is false.