* Show that this is a line integral of a conservative field and use a potential function to evaluate at the curve endpoints. 1. [3x²y²dx + 2x³y dy with C parametrized by x = 3t² + 1 y = 2t 0 ≤t≤1
* Show that this is a line integral of a conservative field and use a potential function to evaluate at the curve endpoints. 1. [3x²y²dx + 2x³y dy with C parametrized by x = 3t² + 1 y = 2t 0 ≤t≤1
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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![* Show that this is a line integral of a conservative field and use a potential function to evaluate at
the curve endpoints.
[3x²y²dx + 2x³ydy with C
1.
★
parametrized by
2. Use Green's Theorem to evaluate the integral
3. Use Stokes' Theorem to compute F. dr
x = 3t² + 1
y = 2t
as
0 ≤t≤1
along C, the boundary of the region lying between y = √x and y = 0 and x = 9
[ f (x²) dx +
(y²) dx + (xy) dy
aQ
dA
[ Pax +Qay = [] (0-2) da
əx
F(x, y, z) = (z², x², y²) on the region bounded by z = 4-x² - y² for z 20
C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb17399b-3b88-4be5-9db3-81af534b05d4%2F1a586825-2f26-4da7-b394-3fccdfbd201d%2F0yscars_processed.jpeg&w=3840&q=75)
Transcribed Image Text:* Show that this is a line integral of a conservative field and use a potential function to evaluate at
the curve endpoints.
[3x²y²dx + 2x³ydy with C
1.
★
parametrized by
2. Use Green's Theorem to evaluate the integral
3. Use Stokes' Theorem to compute F. dr
x = 3t² + 1
y = 2t
as
0 ≤t≤1
along C, the boundary of the region lying between y = √x and y = 0 and x = 9
[ f (x²) dx +
(y²) dx + (xy) dy
aQ
dA
[ Pax +Qay = [] (0-2) da
əx
F(x, y, z) = (z², x², y²) on the region bounded by z = 4-x² - y² for z 20
C
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