Explanation Given: r 2 = cos θ e sin θ Formula Used: The area of a polar curve r = f ( θ ) between two rays θ = α and θ = β will be given by: A r e a ( A ) = 1 2 ∫ α β r 2 d θ Calculation: In the given graph, we can see that the graph is symmetrical with respect to x and y -axis. So, the total area will be two times the area on the right of y-axis and this area has two parts, one part is above the x-axis and the other part is below the x-axis. The above x-axis part is traced between θ = 0 to θ = π 2 . The below x-axis part is traced between 3 π 2 ≤ θ ≤ 2 π So, the total area of the curve is given by: A r e a ( A ) = 2 [ 1 2 ∫ 0 π 2 r 2 d θ + 1 2 ∫

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 12, Problem 35CRE

To determine

The total area enclosed by the curve $r^{2} = \cos θ e^{\sin θ}$ (Figure 2)

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Chapter 12, Problem 34CRE

Chapter 12, Problem 36CRE

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Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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