Finding the Area of the Region Bounded by Two Polar Curves

Next Topic - Infinite Series and Sequences

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) ∫^b_a (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.

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

Question 1 of 8

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

$A = \int_a^b r^2 d\theta$

$A = \frac{1}{2}\int_a^b (r_1^2 - r_2^2) d\theta$

$A = \frac{1}{2}\int_a^b (r_2^2 - r_1^2) d\theta$

$A = \int_a^b (r_2 - r_1) d\theta$

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Finding the Area of the Region Bounded by Two Polar Curves

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