line integral is independent of path by finding a function f such that ∇f = F

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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Show that the line integral is independent of path by finding a function f such that ∇f = F.

2xe−ydx + (2y − x2e−y)dy, C is any path from (1, 0) to (3, 1)
 
 
Evaluate the integral 
 
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