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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 hteplot the (shaded) region over which the integral extends. Finally, compute the value of the integral. (a) ff x²y²dA, 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 < r ≤ sin² 0. (c) √ √³** (x² + y²) dy dx. (d) T [²* (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 hteplot the (shaded) region over which the integral extends. Finally, compute the value of the integral. (a) ff x²y²dA, 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 < r ≤ sin² 0. (c) √ √³** (x² + y²) dy dx. (d) T [²* (x² + y²)3/2 dy dx.

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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Solve c part only now in 30 min pls
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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