   Chapter 16, Problem 6RQ

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.∫−C f (x,y) ds = − ∫C f (x,y) ds

To determine

Whether the statement “ Cf(x,y)ds=Cf(x,y)ds ” is true or false.

Explanation

Consider C is the point on the curve as same as point C, but in opposite orientation of the curve.

Write the expression for Cf(x,y)dx .

Cf(x,y)dx=Cf(x,y)dx

Write the expression for Cf(x,y)dy .

Cf(x,y)dy=Cf(x,y)dy

If f(x,y) is integrated with respect to arc length, then the value of line integral does not change, even though orientation of the curve is reversed

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