91影视

Sketch the vector fields in Exercises 25鈥�32.

$\mathbf{F}(x,y)=-\mathbf{i}+\mathbf{j}$

Evaluate each of the vector field line integrals over the indicated curves.

$\mathbf{F}(x,y)$and $C$are as in Exercise 29, but $C$is traversed in the reverse direction, from$x=10$to$x=5$

Use Green鈥檚 Theorem to evaluate the integral:

$\mathbf{F}(x,y)=xy\mathbf{j}$and C is the square with vertices $(卤3,卤3)$, traversed counterclockwise.

Integrate the given function over the accompanying surface in Exercises 27鈥�34.
$f(x,y,z)=\frac{y}{x}\sqrt{4z^2+1}$, where S is the portion of the paraboloid $z=x^2+y^2$that lies above the rectangle determined by $1鈮�x鈮�e$and $0鈮�y鈮�2$in the xyplane.

${鈭�}_C\mathbf{F}路d\mathbf{r}$,where C is the intersection of the surface z=$e^{-\left(x^2+y^2\right)}$and the cylinder$x^2+y^2=9$and where

Use Green鈥檚 Theorem to evaluate the integrals:

Find ${鈭�}_{C}F.dr$, where $F\left(x,y\right)=\left(x+2y\right)i+\left(x-2y\right)j$and $C$is the boundary of the region bounded by the curves $x=y^2,x=4$, traversed counterclockwise.

${鈭�}_C\mathbf{F}$ - $d\mathbf{r}$, where $\mathrm{C}$ is the intersection of the surface $z=$ $e^{-\left(x^2+y^2\right)}$ and the cylinder $x^2+y^2=9$ and where

$\mathbf{F}(x,y,z)=\ln 鈦�(2x+1)\mathbf{i}+2^{y+1}\mathbf{j}+x{e}^y\mathbf{k}$

$\mathbf{F}(x,y,z)=鉄�xz,yz,xyz)$, and $S$ is the surface of the cylinder with equation $x^2+y^2=9$ for $-2鈮�z鈮�2$.

Sketch the vector fields in Exercises 25鈥�32.

$\mathbf{F}(x,y)=x\mathbf{i}+2y\mathbf{j}$

Use Green鈥檚 Theorem to evaluate the integral for the given vector field and curve.

$F\left(x,y\right)=\left(y^2+1\right)i+2xyj$and C is the circle with equation $x^2+y^2=9$ transversed counterclockwise.