Stokes' Theorem is a generalization of the (a)fundamental theorem of line integrals. (b)flux form of Green's Theorem. (c)circulation form of Green's Theorem.

Use Green’s Theorem to evaluate around the boundary curve C of the region R, where R is the triangle formed by the point (0, 0), (1, 1) and (1, 3).
Find the work done by the force field F(x,y)=4yi+2xj in moving a particle along a circle ${\displaystyle x^2+y^2=1}$ from(0,1)to(1,0).

As Mark Ellon is getting ready for a meeting, the room goes dark. He fishes for a green shirt in his drawer. He wears only blue, green and white colors. His drawers have identical shirts in these colors: 28 blue, 25 green, and 13 white shirts. How many shirts did he throw on the floor to be a cent percent sure that he has a taken out a green shirt?

Using the Divergence Theorem, evaluate ${\displaystyle \int {\int }_{S}F.NdS}$, where ${\displaystyle F(x,y,z)=(z^{3}i-x^{3}j+y^{3}k)}$ and S is the sphere ${\displaystyle x^2+y^2+z^2=a^2}$, with outward unit normal vector N.

Let ${\displaystyle F\overrightarrow{\to }r=<x,y,z>}$ and use the Divergence Theorem to calculate the (nonzero) volume of some solid in IR3 by calculating a surface integral. (You can pick the solid).

Use Greens

Use the Divergence Theorem to calculate the surface integral ${\displaystyle \int {\int }_{S}F·dS}$, that is, calculate the flux of F across S.
${\displaystyle F(x,y,z)=(\cos \left(z\right)+x{y}^2)i+x{e}^{-z}j+(\sin \left(y\right)+x^{2}z)k}$
S is the surface of the solid bounded by the paraboloid ${\displaystyle z=x^2+y^2}$ and the plane z = 9.

Brad and Lena are recording their classmates' eye color for a statistics assignment. In Brad's class, 3 out of the 25 students have green eyes. In Lena's class, 2 out of the 20 students have green eyes. Which class has the greater ratio of green-eyed students to total students?