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81-82. Looking ahead: Area from line integrals The area of a region R in the plane, whose boundary is the curve C, may be computed using line integrals with the formula arca of R = [rdy = - f a |y dx. Let R = {(r, 0): 0 sIs a, 0 s 0 s 2} be the disk of radius a centered at the origin, and let C be the boundary of R oriented counterclockwise. Use the formula A = - Scy dx to verify that the area of the disk is ra².

81-82. Looking ahead: Area from line integrals The area of a region R in the plane, whose boundary is the curve C, may be computed using line integrals with the formula arca of R = [rdy = - f a |y dx. Let R = {(r, 0): 0 sIs a, 0 s 0 s 2} be the disk of radius a centered at the origin, and let C be the boundary of R oriented counterclockwise. Use the formula A = - Scy dx to verify that the area of the disk is ra².

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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81-82. Looking ahead: Area from line integrals The area of a region R in the plane, whose boundary is the curve C, may be computed using line integrals with the formula arca of R = [rdy = - f a |y dx. Let R = {(r, 0): 0 sIs a, 0 s 0 s 2} be the disk of radius a centered at the origin, and let C be the boundary of R oriented counterclockwise. Use the formula A = - Scy dx to verify that the area of the disk is ra².
Transcribed Image Text:81-82. Looking ahead: Area from line integrals The area of a region R in the plane, whose boundary is the curve C, may be computed using line integrals with the formula arca of R = [rdy = - f a |y dx. Let R = {(r, 0): 0 sIs a, 0 s 0 s 2} be the disk of radius a centered at the origin, and let C be the boundary of R oriented counterclockwise. Use the formula A = - Scy dx to verify that the area of the disk is ra².
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