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Finding the Area of the Region Bounded by Two Polar Curves

Abigail Young

Abigail Young

5 min read

Study Guide Overview

This study guide covers finding the area between two polar curves. It reviews the area formula for a single polar curve and introduces the modified formula for two curves: A = (1/2) ∫ba (r22 - r12) dθ. An example problem demonstrates how to identify r1 (inner radius) and r2 (outer radius), determine the integration bounds using the second quadrant, and set up the integral. The guide emphasizes the importance of radians and mentions that complex integrals might require a calculator.

Previous Topic - Find the Area of a Polar Region or the Area Bounded by a Single Polar CurveNext Topic - Infinite Series and Sequences

Question 1 of 8

What is the correct formula to find the area between two polar curves?

A=∫abr2dθA = \int_a^b r^2 d\theta

A=12∫ab(r12−r22)dθA = \frac{1}{2}\int_a^b (r_1^2 - r_2^2) d\theta

A=12∫ab(r22−r12)dθA = \frac{1}{2}\int_a^b (r_2^2 - r_1^2) d\theta

A=∫ab(r2−r1)dθA = \int_a^b (r_2 - r_1) d\theta