A. Let F = P i + Q j be a smooth vector field on R^2 , C a closed simple curve in R^2 , and D the plane simple region enclosed by C. State Green’s Theorem for F, C, and D. B. Evaluate the line integral in Green’s Theorem when F = (x + y)i + xy j and C is the unit circle with equation x^2 + y^2 = 1. C. Evaluate the double integral in Green’s Theorem when F = (x + y)i + xy j, C is the unit circle with equation x 2 + y 2 = 1, and D is the unit disc bounded by C. Then compare your answers in Parts B and C.
A. Let F = P i + Q j be a smooth vector field on R^2 , C a closed simple curve in R^2 , and D the plane simple region enclosed by C. State Green’s Theorem for F, C, and D. B. Evaluate the line integral in Green’s Theorem when F = (x + y)i + xy j and C is the unit circle with equation x^2 + y^2 = 1. C. Evaluate the double integral in Green’s Theorem when F = (x + y)i + xy j, C is the unit circle with equation x 2 + y 2 = 1, and D is the unit disc bounded by C. Then compare your answers in Parts B and C.
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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A. Let F = P i + Q j be a smooth vector field on R^2 , C a closed simple curve in R^2 , and D the plane simple region enclosed by C. State Green’s Theorem for F, C, and D.
B. Evaluate the line integral in Green’s Theorem when F = (x + y)i + xy j and C is the unit circle with equation x^2 + y^2 = 1.
C. Evaluate the double integral in Green’s Theorem when F = (x + y)i + xy j, C is the unit circle with equation x 2 + y 2 = 1, and D is the unit disc bounded by C. Then compare your answers in Parts B and C.
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