Question

Use Stokes' theorem to evaluate $\iint_S curl(\mathbf{F}) \cdot d\mathbf{S}$. $\mathbf{F}(x, y, z) = e^{3xy}\mathbf{i} + e^{xz}\mathbf{j} + x^2z\mathbf{k}$, $S$ is the half of the ellipsoid $4x^2 + y^2 + 4z^2 = 4$ that lies to the right of the xz-plane, oriented in the direction of the positive y-axis.

Name: use stokes theorem to evaluate iints curlmathbff cdot dmathbfs mathbffx y z e3xymathbfi exzmathbfj x2zmathbfk s is the half of the ellipsoid 4x2 y2 4z2 4 that lies to the right of the xz pl 92409
Uploaded: 2021-05-24T14:30:43-08:00
Duration: 2 min 12 s
Channel: Vikash Ranjan
Description: use stokes theorem to evaluate iints curlmathbff cdot dmathbfs mathbffx y z e3xymathbfi exzmathbfj x2zmathbfk s is the half of the ellipsoid 4x2 y2 4z2 4 that lies to the right of the xz pl 92409

          Use Stokes' theorem to evaluate $\iint_S curl(\mathbf{F}) \cdot d\mathbf{S}$.
$\mathbf{F}(x, y, z) = e^{3xy}\mathbf{i} + e^{xz}\mathbf{j} + x^2z\mathbf{k}$, $S$ is the half of the ellipsoid $4x^2 + y^2 + 4z^2 = 4$ that lies to the right of the xz-plane, oriented in the direction of the positive y-axis.

use stokes theorem to evaluate iints curlmathbff cdot dmathbfs mathbffx y z e3xymathbfi exzmathbfj x2zmathbfk s is the half of the ellipsoid 4x2 y2 4z2 4 that lies to the right of the xz pl 92409

Added by Scott C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vikash Ranjan

05/24/2021

Step 1

The boundary of $S$ is the ellipse $4x^2 + y^2 + 4z^2 = 4$ in the $xz$-plane, which is $4x^2 + 0^2 + 4z^2 = 4$, or $x^2 + z^2 = 1$. Since $S$ is oriented in the direction of the positive $y$-axis, the boundary $C$ is oriented counterclockwise when viewed from the Show more…

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Use Stokes' theorem to evaluate $\iint_S curl(\mathbf{F}) \cdot d\mathbf{S}$. $\mathbf{F}(x, y, z) = e^{3xy}\mathbf{i} + e^{xz}\mathbf{j} + x^2z\mathbf{k}$, $S$ is the half of the ellipsoid $4x^2 + y^2 + 4z^2 = 4$ that lies to the right of the xz-plane, oriented in the direction of the positive y-axis.