$(1$ point$)$ Use Stokes' Theorem to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$

where $F(x,y,z)=($:$6x+y^2,y+z^2,2z+x^2$:$)$ and $C$ is the triangle with vertices $(1,0,0),(0,1,0),$ and $(0,0,1)$ oriented counterclockwise as viewed from above.

Since the triangle is oriented counterclockwise as viewed from above the surface we attach to the triangle is oriented

cu

The easiest surface to attach to this curve is the interior of the triangle. Using this surface in Stokes' Theorem evaluate the following.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr={\displaystyle \underset{x_1}{\overset{x_2}{}}}{\displaystyle \underset{y_1}{\overset{y_2}{}}}$

where

$,y_1=$

$y_2=$

$x_1=$

$x_2=$

$dydx$

Evaluate

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr=$