Explanation Given: The values of r are r = 2 + 2 cos θ and r = 1 . Calculation: From the given equations, draw the graph. Since we have two values for the radius, we first draw the two circles with the given equations by performing the following steps: Draw the reference axis in polar coordinates. Find the values of r for θ = 0 , π 6 , π 4 , π 3 , π 2 θ r 1 = 1 r 2 = 2 + 2 cos θ ( r 1 , θ ) , ( r 2 , θ ) 0 1 4 ( 1 , 0 ) , ( 4 , 0 ) π 6 1 2 + 3 ( 1 , π 6 ) , ( 2 + 3 , π 6 ) π 4 1 2+ 2 ( 1 , π 4 ) , ( 2 + 2 , π 4 ) π 3 1 3 ( 1 , π 3 ) , ( 3 , π 3 ) π 2 1 2 ( 1 , π 2 ) , ( 2 , π 2 ) Mark the points on the plot and connect the points. Use the symmetry to complete the graph for the given limit, that is, θ = 2 π . The area of integration lies within the limits of the integral, so shade according to the given conditions. The final plot is shown below:

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ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.3, Problem 48E

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To calculate: The area of the shaded region by plotting a graph using the equation r=2+2cosθ and r=1.

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Chapter 14.3, Problem 47E

Chapter 14.3, Problem 49E

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The area of the shaded region by plotting a graph using the equation r = 2 + 2 cos θ and r = 1 .

Solution Summary: The author explains how to calculate the area of the shaded region by plotting a graph using the equation r=2+2mathrmcostheta .

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To calculate: The area of the shaded region by plotting a graph using the equation r=2+2cosθ and r=1.

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Chapter 14 Solutions