Answer to Question #120953 in Calculus for Olivia

Question

If all the assumptions in Green's Theorem are satisfied, which of the following statements is true about Green's Theorem?
Select one:
a. The result in Green's Theorem provides a relationship between line integrals and conservative vector fields.
b. The result in Green's Theorem provides a relationship between line integrals and gradient vector fields.
c. The result in Green's Theorem provides a relationship between line integrals and double integrals.
d. The result in Green's Theorem provides a relationship between line integrals and triple integrals.

Answer 1

We can convert line integral to surface integral by using stock's theorem .....(1)

Now on surface integral which is obtained by (1) we can apply green's theorem which convert surface to volume integral ....(2)

Now we can say that green's theorem gives relation between line and volume integral.

Ans. Option (4).