   Chapter 16, Problem 5RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If F = P i + Q j and Py = Qx in an open region D. then F is conservative.

To determine

Whether the statement “If F=Pi+Qj and Py=Qx in an open region D, then F is conservative” is true or false.

Explanation

If every simple closed curve in D encloses only points that are present in D then, the connected region is known as simply-connected region.

Consider the vector field F=Pi+Qj is open and simply connected to region D.

If P and Q are continuous first-order partial derivatives and Py=Qx throughout the region D then the vector function F is conservative

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