Example

Video Example $4.$

Find the area enclosed by one loop of the four$-$leafed rose $r=9cos({25}^5).$

Solution

$$

$={\displaystyle \underset{-\frac{}{4}}{\overset{\frac{}{4}}{}}}{2}^{2}dt$

$=\frac{1}{2}{\displaystyle \underset{-\frac{}{4}}{\overset{\frac{}{4}}{}}}()d$

$=81{\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}({]}_0^{\frac{}{4}}\frac{1}{2}(1cos(40))d$

$=81{\displaystyle \underset{0}{\overset{\frac{}{4}}{}}}$

$=\frac{81}{2}$

$=\frac{?}{2}$