   Chapter 16.3, Problem 30E

Chapter
Section
Textbook Problem

Use Exercise 29 to show that the line integral ∫C y dx + x dy + xyz dz is not independent of path.

To determine

To show: The line integral Cydx+xdy+xyzdz is not independent of path.

Explanation

Given data:

Line integral is Cydx+xdy+xyzdz .

Formula used:

When a vector field F=Pi+Qj+Rk is conservative, then there exist a potential function such that F=f and the integral of vector field is independent of path.

The essential conditions for vector field is being conservative are,

Py=Qx ,

Pz=Rx , and

Qz=Ry

Compare the integrals Cfdr and Cydx+xdy+xyzdz .

f=yi+xj+xyzk

Compare the equation f=yi+xj+xyzk with F=Pi+Qj+Rk

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Evaluate the integral by interpreting it in terms of areas. 55(x=25x2)dx

Single Variable Calculus: Early Transcendentals, Volume I

Rectangular coordinates of the point with polar coordinates are: (−1, 0) (0, 1) (0, −1) (1, 0)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find if , y = sin 2t.

Study Guide for Stewart's Multivariable Calculus, 8th 