Explanation Result used: The area inside the polar curve r = f ( θ ) over the interval [ α , β ] is given by A = ∫ α β 1 2 f ( θ ) 2 d θ . Calculation: The given equations of the polar curves are r = 1 − cos θ and r = 1 + cos θ . Use online graphing calculator and draw the graph of r = 1 − cos θ and r = 1 + cos θ as shown below in Figure 1. In Figure 1, the shaded region is the required region. Consider the area in the first quadrant. Total area is 4 times the area in the first quadrant. From Figure 1 it is noted that the region in the first quadrant is generated when θ varies from 0 to π 2 . Therefore, the area A 1 is, A 1 = ∫ 0 π 2 1 2 ( 1 − cos θ ) 2 d θ = 1 2 ∫ 0 π 2 ( 1 − 2 cos θ + cos 2 θ ) d θ = 1 2 [ ∫ 0 π 2 d θ − 2 ∫ 0 π 2 cos θ d θ + ∫ 0 π 2 ( 1 + cos 2 θ 2 ) d θ ] [ ∵ cos 2 θ = 1 + cos 2 θ 2 ] = 1 2 [ <

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ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Chapter 10, Problem 36RE

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To find: The area of the region that is inside the cardiods r=1−cosθ and r=1+cosθ with the help of the sketch of the region and its bounding curves.

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Chapter 10, Problem 35RE

Chapter 10, Problem 37RE

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The area of the region that is inside the cardiods r = 1 − cos θ and r = 1 + cos θ with the help of the sketch of the region and its bounding curves.

Solution Summary: The author explains the area of the region inside the cardiods r=1-mathrmcostheta and its bounding curves using an online graphing calculator.

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To find: The area of the region that is inside the cardiods r=1−cosθ and r=1+cosθ with the help of the sketch of the region and its bounding curves.

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Chapter 10 Solutions