Question

(1 point) Use Stokes' Theorem to evaluate $iint_S ext{curl } mathbf{F} cdot dmathbf{S}$ ewline where $mathbf{F}(x, y, z) = e^{xy}mathbf{i} - 2e^{xz}mathbf{j} + 4x^2zmathbf{k}$ and $S$ is the half of the ellipsoid $x^2 + y^2 + z^2 = 1$ that lies to the right of the $xz$-plane, oriented in the ewline direction of the positive $y$-axis. ewline Since the half ellipsoid is oriented in the direction of the positive $y$-axis the boundary curve must be transversed clockwise when viewed ewline from the left. ewline A parametrization for the boundary curve $C$ can be given by: ewline $mathbf{r}(t) = cos(t)mathbf{i} + ext{ }mathbf{j} + ext{ }mathbf{k}$, $0 le t le ext{ }$ ewline (use the most natural parametrization) ewline $iint_S ext{curl } mathbf{F} cdot dmathbf{S} = int_0^b ext{ }dt$ ewline $iint_S ext{curl } mathbf{F} cdot dmathbf{S} = $

          (1 point) Use Stokes' Theorem to evaluate $iint_S 	ext{curl } mathbf{F} cdot dmathbf{S}$ 
ewline where $mathbf{F}(x, y, z) = e^{xy}mathbf{i} - 2e^{xz}mathbf{j} + 4x^2zmathbf{k}$ and $S$ is the half of the ellipsoid $x^2 + y^2 + z^2 = 1$ that lies to the right of the $xz$-plane, oriented in the 
ewline direction of the positive $y$-axis. 
ewline Since the half ellipsoid is oriented in the direction of the positive $y$-axis the boundary curve must be transversed clockwise when viewed 
ewline from the left. 
ewline A parametrization for the boundary curve $C$ can be given by: 
ewline $mathbf{r}(t) = cos(t)mathbf{i} + 	ext{ }mathbf{j} + 	ext{ }mathbf{k}$, $0 le t le 	ext{ }$ 
ewline (use the most natural parametrization) 
ewline $iint_S 	ext{curl } mathbf{F} cdot dmathbf{S} = int_0^b 	ext{ }dt$ 
ewline $iint_S 	ext{curl } mathbf{F} cdot dmathbf{S} = $

(1 point) Use Stokes' Theorem to evaluate iintS extcurl mathbfF cdot dmathbfS
ewline where mathbfF(x, y, z) = e^xymathbfi - 2e^xzmathbfj + 4x^2zmathbfk and S is the half of the ellipsoid x^2 + y^2 + z^2 = 1 that lies to the right of the xz-plane, oriented in the
ewline direction of the positive y-axis.
ewline Since the half ellipsoid is oriented in the direction of the positive y-axis the boundary curve must be transversed clockwise when viewed
ewline from the left.
ewline A parametrization for the boundary curve C can be given by:
ewline mathbfr(t) = cos(t)mathbfi + extmathbfj + extmathbfk, 0 le t le ext
ewline (use the most natural parametrization)
ewline iintS extcurl mathbfF cdot dmathbfS = int0^b extdt
ewline iintS extcurl mathbfF cdot dmathbfS =

Added by Shawn G.

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