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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

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 2E
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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
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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