HH_Sec_8_3 - r = 4 sin , in Figure 1. 2-2 r 2 r = 4 sin...

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(9/30/08) Math 10B. Lecture Examples. Section 8.3. Area and arc length in polar coordinates Example 1 Sketch the curve in an xy -plane with the polar equation r = 1 + cos θ, 0 θ 2 π . (The curve is called a cardioid because of its heart-like shape.) Answer: Figures A1a, A1b, and A1c θ r 1 2 π 2 π r = 1 + cos θ 1 2 π 3 2 π x 1 y - 1 1 r θ x 1 y - 1 1 r = 1 + cos θ r = 1 + cos θ in an -plane The cardioid for 0 t 1 2 π The entire cardioid Figure A1a Figure A1b Figure A1c Example 2 Find the area of the region bounded by the cardioid from Example 1 with polar equation r = 1 + cos θ, 0 θ 2 π . (Use the identity cos 2 θ = 1 2 [ 1 + cos ( 2 θ )] in the integration.) Answer: [Area] = 3 2 π Example 3 Use polar coordinates to ±nd the area bounded by the circle
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Unformatted text preview: r = 4 sin , in Figure 1. 2-2 r 2 r = 4 sin FIGURE 1 Interactive Examples Work the following Interactive Examples on Shenks web page, http//www.math.ucsd.edu/ashenk/: Section 11.3: Examples 15 Lecture notes to accompany Section 8.3 of Calculus by Hughes-Hallett et al. The chapter and section numbers on Shenks web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. 1...
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This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

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