Answer to Question #120951 in Calculus for Olivia

Question

Which of the following statements is true about line integrals?
Select one:
a. ∫−C F⋅dr=−2∫C F⋅dr


b. ∫−C F⋅dr=0


c. ∫−C F⋅dr=∫C F⋅dr


d. ∫−C F⋅dr=−∫C F⋅dr

Answer 1

If C is a curve and -C is the same curve which is traversed in the opposite direction, then,

$\int_{-C} F.dr =- \int_C F.dr$

because reversing the direction of the curve from C to. -C changes the sign where F is the vector field.

The correct answer is OptionD.