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Problem 8.2. Each part of this problem contains a double integral. In each case, you should first convert to polar coordinates. Next, use the polarRegion program from Chr plot the (shaded) region over which the integral extends. Finally, compute the value of the integral. (a) ff x²y² dA, where R is the inside of the cardioid r = 2(1 + sin 0). (b) ff cos(x² + y²) dA, where R is defined by 0 ≤ 0 ≤/2 and 0 ≤ ≤ sin²0. √√9-x² (c) › ³²³** (x² + y²) dy dx. Salo (d) [+ (x² + y²)³/2 dy dx.

Problem 8.2. Each part of this problem contains a double integral. In each case, you should first convert to polar coordinates. Next, use the polarRegion program from Chr plot the (shaded) region over which the integral extends. Finally, compute the value of the integral. (a) ff x²y² dA, where R is the inside of the cardioid r = 2(1 + sin 0). (b) ff cos(x² + y²) dA, where R is defined by 0 ≤ 0 ≤/2 and 0 ≤ ≤ sin²0. √√9-x² (c) › ³²³** (x² + y²) dy dx. Salo (d) [+ (x² + y²)³/2 dy dx.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 10DE
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Problem 8.2. Each part of this problem contains a double integral. In each case, you should first convert to polar coordinates. Next, use the polarRegion program from Our plot the (shaded) region over which the integral extends. Finally, compute the value of the integral. (a) ffx²y²dA, where R is the inside of the cardioid r = 2(1 + sin 0). (b) ff cos(x² + y²) dA, where R is defined by 0 ≤ 0 ≤/2 and 0 ≤ ≤ sin²0. -3 √9-x² (c) › ³²³** (x² + y²) dy dx. SA SO (d) [+ (x² + y²)³/2 dy dx.
Transcribed Image Text:Problem 8.2. Each part of this problem contains a double integral. In each case, you should first convert to polar coordinates. Next, use the polarRegion program from Our plot the (shaded) region over which the integral extends. Finally, compute the value of the integral. (a) ffx²y²dA, where R is the inside of the cardioid r = 2(1 + sin 0). (b) ff cos(x² + y²) dA, where R is defined by 0 ≤ 0 ≤/2 and 0 ≤ ≤ sin²0. -3 √9-x² (c) › ³²³** (x² + y²) dy dx. SA SO (d) [+ (x² + y²)³/2 dy dx.
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