Introduction to Electrodynamics · Problem 1.29

Vector Analysis — David J. Griffiths

Physics · vector-calculus-line-integrals

Problem

Calculate the line integral of the function

\mathbf{v} = x^2\,\hat{\mathbf{x}} + 2yz\,\hat{\mathbf{y}} + y^2\,\hat{\mathbf{z}}

from the origin to the point

(1,1,1)

by three different routes: (a)

(0,0,0) \to (1,0,0) \to (1,1,0) \to (1,1,1)

. (b)

(0,0,0) \to (0,0,1) \to (0,1,1) \to (1,1,1)

. (c) The direct straight line. (d) What is the line integral around the closed loop that goes out along path (a) and back along path (b)?