AP Calculus BC 9.8 Polar Areas Overview

Review polar-area questions by identifying bounds and integrating one half r squared over the relevant angular interval.

Covered syllabus points

CHA-5.D—Calculate areas of regions defined by polar curves using definite integrals

[Maximum number: 2]

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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Covered syllabus points

9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve question 1