Show F(x, y) = (2xy³ + 8)i + (3æ²y² + 2e2")j is conservative by finding a potential function f for F, and use f to compute F. dr, where C is the curve given by 2t r(t) = (2 sin° t)i + ( sin°(54) ) j for 0 < t < 1/2. f(x, y) = | x^2y^3+8x+e^(2y) F. dr = 2e^2+19
Show F(x, y) = (2xy³ + 8)i + (3æ²y² + 2e2")j is conservative by finding a potential function f for F, and use f to compute F. dr, where C is the curve given by 2t r(t) = (2 sin° t)i + ( sin°(54) ) j for 0 < t < 1/2. f(x, y) = | x^2y^3+8x+e^(2y) F. dr = 2e^2+19
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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Need help with cal-3
Transcribed Image Text:Show
F(x, y)
= (2xy³ + 8)i + (3æ?y? + 2e²")j
is conservative by finding a potential function f for F, and use f to compute
F. dr, where C is the curve given by
r(t) = 2 sin" t)i +
( sin° (54) ) i
for 0 <t< п/2.
f(x, y) = x^2y^3+8x+e^(2y)
F. dr =
2e^2+19
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