   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

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