Answer
$=18$
Work Step by Step
Given: $r^2=9 cos 5 \theta$
$Area,A=\int_{- \pi/10}^{\pi/10}\frac{r^2}{2}d\theta$
$=\int_{- \pi/10}^{\pi/10}\dfrac{9cos5 \theta}{2}d\theta$
$=10[\dfrac{9sin5 \theta}{10}]_{- \pi/10}^{\pi/10}$
$=18$
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