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  3. ZuAI AP College Board Calculus AB/BC
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Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

Abigail Young

Abigail Young

6 min read

Study Guide Overview

This guide covers calculating the area of polar regions using definite integrals. It explains polar coordinates and their relation to Cartesian coordinates. The guide details the formula for area calculation, using the sector method with examples like circles and rose curves. It also demonstrates using symmetry to simplify calculations and provides a practice problem involving a limaçon curve.

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Question 1 of 8

In polar coordinates, a point is located 3 units from the origin at an angle of π2\frac{\pi}{2}2π​ radians. Which of the following correctly represents this point?

(3,π2)(3, \frac{\pi}{2})(3,2π​)

(3,0)(3, 0)(3,0)

(0,π2)(0, \frac{\pi}{2})(0,2π​)

(π2,3)(\frac{\pi}{2}, 3)(2π​,3)