Evaluate the surface integral ${\displaystyle \underset{S}{\overset{\phantom{}}{}}}F*dS$ where $F=($:$x,-4z,4y$:$)$ and $S$ is the part of the sphere $x^2+y^2+z^2=16$ in the first octant, with orientation toward the origin.

${}_{S}F*dS=$

Calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2(x^2-y)(vec(i))+7(y^2+x)(vec(j)))*dvec(r)$ if:

$($a$)C$ is the circle $(x-6{)}^2+(y-2{)}^2=9$ oriented counterclockwise.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2(x^2-y)(vec(i))+7(y^2+x)(vec(j)))*dvec(r)=$

$($b$)C$ is the circle $(x-a{)}^2+(y-b{)}^2=R^2$ in the $xy-$plane oriented counterclockwise.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2(x^2-y)(vec(i))+7(y^2+x)(vec(j)))*dvec(r)=$

Calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2(x^2-y)(vec(i))+7(y^2+x)(vec(j)))*dvec(r)$ if:

$($a$)C$ is the circle $(x-6{)}^2+(y-2{)}^2=9$ oriented counterclockwise.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2(x^2-y)(vec(i))+7(y^2+x)(vec(j)))*dvec(r)=$

$($b$)C$ is the circle $(x-a{)}^2+(y-b{)}^2=R^2$ in the $xy-$plane oriented counterclockwise.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}(2(x^2-y)(vec(i))+7(y^2+x)(vec(j)))*dvec(r)=$