Solve the Line Integral with the Fundamental Theorem of Line Integrals - 16.3.14 Cengage

Problem 16.3: 14, Cengage Calculus 9th Edition
Cengage Calculus, 9th Edition Chapter 16: Vector Calculus 16.4 The Fundamental Theorem for Line Integrals, problem 14, 16.3.14, 14–15 A vector field and a curve are given. Show that is conservative and find a potential function . Evaluate using Theorem 2. Evaluate by first replacing with a line segment that has the same initial and terminal points. Let and let be the curve shown. Evaluate directly. Answer Show that is conservative and find a function such that Answer Evaluate using Theorem 2. Evaluate by first replacing by a simpler curve that has the same initial and terminal points.