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Show that the line integral is independent of path. 2xe dx + (2y-x²e)dy, C is any path from (1, 0) to (3, 1) The functions 2xe- and 2y - x²ey have continuous first-order derivatives on R² and (2xe-x) = integral is independent of path. ap ay Theorem: Let F = Pi + Qj be a vector field on an open simply-connected region D. Suppose that P and Q have continuous first-order partial derivatives and Evaluate the integral. =(2y - x²-y), so F(x, y) = i + (2y - x²e)j is a conservative vector field by the theorem given below, hence the line ax throughout D. Then F is conservative.

Show that the line integral is independent of path. 2xe dx + (2y-x²e)dy, C is any path from (1, 0) to (3, 1) The functions 2xe- and 2y - x²ey have continuous first-order derivatives on R² and (2xe-x) = integral is independent of path. ap ay Theorem: Let F = Pi + Qj be a vector field on an open simply-connected region D. Suppose that P and Q have continuous first-order partial derivatives and Evaluate the integral. =(2y - x²-y), so F(x, y) = i + (2y - x²e)j is a conservative vector field by the theorem given below, hence the line ax throughout D. Then F is conservative.

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.CR: Chapter 6 Review
Problem 37CR
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Show that the line integral is independent of path. Jo 2xe Ydx + (2y x²e-)dy, C is any path from (1, 0) to (3, 1) The functions 2xe Y and 2y - x²ey have continuous first-order derivatives on R² and (2xe-x) = integral is independent of path. მ ду -x²e), so F(x, y) = Evaluate the integral. i + (2y - x²e¯)j is a conservative vector field by the theorem given below, hence the line ap მდ Theorem: Let F = Pi + Qj be a vector field on an open simply-connected region D. Suppose that P and Q have continuous first-order partial derivatives and = throughout D. Then F is conservative. ay ?x
Transcribed Image Text:Show that the line integral is independent of path. Jo 2xe Ydx + (2y x²e-)dy, C is any path from (1, 0) to (3, 1) The functions 2xe Y and 2y - x²ey have continuous first-order derivatives on R² and (2xe-x) = integral is independent of path. მ ду -x²e), so F(x, y) = Evaluate the integral. i + (2y - x²e¯)j is a conservative vector field by the theorem given below, hence the line ap მდ Theorem: Let F = Pi + Qj be a vector field on an open simply-connected region D. Suppose that P and Q have continuous first-order partial derivatives and = throughout D. Then F is conservative. ay ?x
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