Use Green's Theorem to evaluate [ F. dr, where F = (√x + 8y, 6x + √√y) - C consists of the arc of the curve y = 7x − x² from (0, 0) to (7,0) and the line segment from (7,0) to (0,0). Hint: Check the orientation of the curve before applying the theorem. (a) Convert the given integral to a double integral using Green's Theorem. Remember to account for the curve orientation.
Use Green's Theorem to evaluate [ F. dr, where F = (√x + 8y, 6x + √√y) - C consists of the arc of the curve y = 7x − x² from (0, 0) to (7,0) and the line segment from (7,0) to (0,0). Hint: Check the orientation of the curve before applying the theorem. (a) Convert the given integral to a double integral using Green's Theorem. Remember to account for the curve orientation.
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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Transcribed Image Text:Use Green's Theorem to evaluate
[ F. dr, where
C
F = (√x + 8y, 6x + √√y)
C consists of the arc of the curve y = 7x − x² from (0, 0) to (7,0) and the line segment from (7,0) to
(0,0).
Hint: Check the orientation of the curve before applying the theorem.
(a) Convert the given integral to a double integral using Green's Theorem. Remember to account for the
curve orientation.
dy dx
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