AP Calculus BC Cha 5 D Calculate Areas of Regions Defined By Polar Curves Using Definite Integrals Questions

Practice AP Calculus BC questions on using one-half r-squared integrals to find areas bounded by polar curves in context.

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Let S be the region bounded by the graph of the polar curve $r(\theta)=3 \sqrt{\theta} \sin \left(\theta^{2}\right)$ for $0 \leq \theta \leq \sqrt{\pi}$ , as shown in the figure above.

Find the area of S.

$\frac{1}{2} \int_{0}^{\sqrt{\pi}}(r(\theta))^{2} d \theta=3.534292$
The area of S is 3.534.

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AP Calculus BC Cha 5 D Calculate Areas of Regions Defined By Polar Curves Using Definite Integrals Questions question 1