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6 Evaluate (3x+4yʻ) dA by changing to polar coordinates, where R is the region in the upper half-plane R ahat liae hetween the circles x +y = 1 and x + y = 4. %3D

6 Evaluate (3x+4yʻ) dA by changing to polar coordinates, where R is the region in the upper half-plane R ahat liae hetween the circles x +y = 1 and x + y = 4. %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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This problem is already solved, can you rewrite the problem in clear steps to get the same answer? It’s not completely clear to me. thank you.
I| (3x+4y´) dA by changing to polar coordinates, where R is the region in the upper half-plane 6. Evaluate alant liec hetween the circles x+ v} = 1 and x² + v? = 4. 6. The region R can be described as R={(x, y) | y= 0, 1< x + y° < 4} It is a half-ring, and in polar coordinates it is given by 1 <r2, 0 < 0 < T. r+y = 4 r+y = 1 Therefore, || (3x + 4y2) dA = (3rcos 0 + 4r² sin 0) r dr de 3r cos e + 4r° sin*e) dr de cos e+ r* sin e| de =" (7 cos e + 15 sin e) de cos +(1 – cos 20) de 15 150 =D7 sin 0+ 15 sin 20 4
Transcribed Image Text:I| (3x+4y´) dA by changing to polar coordinates, where R is the region in the upper half-plane 6. Evaluate alant liec hetween the circles x+ v} = 1 and x² + v? = 4. 6. The region R can be described as R={(x, y) | y= 0, 1< x + y° < 4} It is a half-ring, and in polar coordinates it is given by 1 <r2, 0 < 0 < T. r+y = 4 r+y = 1 Therefore, || (3x + 4y2) dA = (3rcos 0 + 4r² sin 0) r dr de 3r cos e + 4r° sin*e) dr de cos e+ r* sin e| de =" (7 cos e + 15 sin e) de cos +(1 – cos 20) de 15 150 =D7 sin 0+ 15 sin 20 4
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