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For the two leaf rose r = 1 + cos(20) and cardioids r = 1 + sin(0) and r = 1 - sin() shown in the figure. Use double integration in Polar coordinates to find the shaded area. r-1 sin(0) Useful formulas: cos(20) = 1- 2 sin² 0 r=1+ cos (20) 1 + cos 20 (cos2 (0) = = 2 1- cos 20 sin² (8) 2 r-1-sin(0)

For the two leaf rose r = 1 + cos(20) and cardioids r = 1 + sin(0) and r = 1 - sin() shown in the figure. Use double integration in Polar coordinates to find the shaded area. r-1 sin(0) Useful formulas: cos(20) = 1- 2 sin² 0 r=1+ cos (20) 1 + cos 20 (cos2 (0) = = 2 1- cos 20 sin² (8) 2 r-1-sin(0)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For the two leaf rose r = 1 + cos(20) and cardioids r = 1 + sin(0) and r = 1 - sin() shown in the figure. Use double integration in Polar coordinates to find the shaded area. r-1* sin(0) Useful formulas: cos(20) = 1- 2 sin² 0 r=1+ cos (20) 1 + cos 20 (cos² (0) 2 1- cos 20 sin² (8) = 2 = r- 1-sin(0)
Transcribed Image Text:For the two leaf rose r = 1 + cos(20) and cardioids r = 1 + sin(0) and r = 1 - sin() shown in the figure. Use double integration in Polar coordinates to find the shaded area. r-1* sin(0) Useful formulas: cos(20) = 1- 2 sin² 0 r=1+ cos (20) 1 + cos 20 (cos² (0) 2 1- cos 20 sin² (8) = 2 = r- 1-sin(0)
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