[Green's Theorem] Practice using Green's Theorem by calculating the following line integrals; we can use Green's theorem because these are work integrals around loops in R². (a) Calculate $1 F-dr, where F(x, y) = (x5 +3ry, 2x + y²), where C is the piecewise linear loop from (0,0) - to (1,0) to (0,2) back to (0,0). e f F F-dr, where C is the path from (1,0) to (0,0) to (0, 1) along straight lines and then back to (1,0) along the quarter of the unit circle, and F(x, y) = (2y+e")i + (x³ - siny).j. - (b) Calculate e fF-dr, where F(x, y) = (2xy², y³), where C is the piecewise loop from (0,0) to (1, 1) along (c) Calculate y-√, then along the linear path from (1, 1) to (2,0), then along the z-axis back to (0,0). (d) Calculate F-dr, where F(x, y) = (2rye ²)i + (x²e-v² – 2x²y²e)j, where C is the path from (2,0) to (-2,0) along y 4-², then back to (2,0) along the z-axis. $1 C
[Green's Theorem] Practice using Green's Theorem by calculating the following line integrals; we can use Green's theorem because these are work integrals around loops in R². (a) Calculate $1 F-dr, where F(x, y) = (x5 +3ry, 2x + y²), where C is the piecewise linear loop from (0,0) - to (1,0) to (0,2) back to (0,0). e f F F-dr, where C is the path from (1,0) to (0,0) to (0, 1) along straight lines and then back to (1,0) along the quarter of the unit circle, and F(x, y) = (2y+e")i + (x³ - siny).j. - (b) Calculate e fF-dr, where F(x, y) = (2xy², y³), where C is the piecewise loop from (0,0) to (1, 1) along (c) Calculate y-√, then along the linear path from (1, 1) to (2,0), then along the z-axis back to (0,0). (d) Calculate F-dr, where F(x, y) = (2rye ²)i + (x²e-v² – 2x²y²e)j, where C is the path from (2,0) to (-2,0) along y 4-², then back to (2,0) along the z-axis. $1 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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Can you please help me with parts A - D?
![6. [Green's Theorem] Practice using Green's Theorem by calculating the following line integrals; we can use
Green's theorem because these are work integrals around loops in R².
(a) Calculate
F-dr, where F(x, y) = (x² + 3xy, 2x + y2), where C is the piecewise linear loop from (0,0)
to (1,0) to (0,2) back to (0,0).
(b) Calculate F-dr, where C is the path from (1,0) to (0,0) to (0, 1) along straight lines and then back
to (1,0) along the quarter of the unit circle, and F(x, y) = (2y +eª)i + (x³ — sin y).j.
-
(c) Calculate F-dr, where F(x, y) = (2ry², y³), where C is the piecewise loop from (0,0) to (1, 1) along
C
y-√√, then along the linear path from (1, 1) to (2,0), then along the z-axis back to (0,0).
=
e f F F-dr, where F(x, y) — (2rye¯³²)i + (x²e¯²-2r²y²e²)j, where C is the path from (2,0)
to (-2,0) along y - 4-z², then back to (2,0) along the z-axis.
(d) Calculate](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34e6895f-8abd-4c7c-a38e-4b1b563dc71a%2Ff24fa931-bd16-44ef-b46b-2f11eec12ed3%2Fbrozkca_processed.png&w=3840&q=75)
Transcribed Image Text:6. [Green's Theorem] Practice using Green's Theorem by calculating the following line integrals; we can use
Green's theorem because these are work integrals around loops in R².
(a) Calculate
F-dr, where F(x, y) = (x² + 3xy, 2x + y2), where C is the piecewise linear loop from (0,0)
to (1,0) to (0,2) back to (0,0).
(b) Calculate F-dr, where C is the path from (1,0) to (0,0) to (0, 1) along straight lines and then back
to (1,0) along the quarter of the unit circle, and F(x, y) = (2y +eª)i + (x³ — sin y).j.
-
(c) Calculate F-dr, where F(x, y) = (2ry², y³), where C is the piecewise loop from (0,0) to (1, 1) along
C
y-√√, then along the linear path from (1, 1) to (2,0), then along the z-axis back to (0,0).
=
e f F F-dr, where F(x, y) — (2rye¯³²)i + (x²e¯²-2r²y²e²)j, where C is the path from (2,0)
to (-2,0) along y - 4-z², then back to (2,0) along the z-axis.
(d) Calculate
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