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4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is the arc of the hyperbola y = from (1, 1) to (4,1). (b) F(x, y) = yzez î+eªz ĵ + xye™z Ê, C: r(t) = (t² + 1) î+ (t² − 1) ĵ + (t² −2t) k, 0≤ t ≤ 2.

4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is the arc of the hyperbola y = from (1, 1) to (4,1). (b) F(x, y) = yzez î+eªz ĵ + xye™z Ê, C: r(t) = (t² + 1) î+ (t² − 1) ĵ + (t² −2t) k, 0≤ t ≤ 2.

Advanced Engineering Mathematics
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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4. Find f such that F = Vf and use it to evaluate fF.dr. (a) F(x, y) = (3 + 2xy²) î+2x²y ĵ, C is the arc of the hyperbola y = from (1, 1) to (4, ½). (b) F(x, y) = yze™z î+ eªz ĵ+ xye™z Ê, C: r(t) = (t² + 1) î + (t² − 1) ĵ + (t² − 2t) Ê, 0 ≤ t ≤ 2. - -
Transcribed Image Text:4. Find f such that F = Vf and use it to evaluate fF.dr. (a) F(x, y) = (3 + 2xy²) î+2x²y ĵ, C is the arc of the hyperbola y = from (1, 1) to (4, ½). (b) F(x, y) = yze™z î+ eªz ĵ+ xye™z Ê, C: r(t) = (t² + 1) î + (t² − 1) ĵ + (t² − 2t) Ê, 0 ≤ t ≤ 2. - -
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