6. Let S denote the disc of radius 2 that is centered at the point (0, 0,3) and parallel to the X-Y plane, oriented so that the top of S points in the direction of the negative Z-axis. Compute ff, F. dr where F(x, y, z) = x+sin(y) 2³-xyz z+y-1
6. Let S denote the disc of radius 2 that is centered at the point (0, 0,3) and parallel to the X-Y plane, oriented so that the top of S points in the direction of the negative Z-axis. Compute ff, F. dr where F(x, y, z) = x+sin(y) 2³-xyz z+y-1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![6. Let \( S \) denote the disc of radius 2 that is centered at the point \( (0, 0, 3) \) and parallel to the \( X-Y \) plane, oriented so that the top of \( S \) points in the direction of the negative \( Z \)-axis. Compute \(\iint_{S} \vec{F} \cdot d\vec{r}\) where
\[
\vec{F}(x, y, z) = \begin{pmatrix} x + \sin(y) \\ z^3 - xyz \\ z + y - 1 \end{pmatrix}.
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc158a850-76a9-4504-97b9-8593e0926539%2Fbd381025-7734-41e4-88b0-9473b95a6566%2Fiwu5s1n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Let \( S \) denote the disc of radius 2 that is centered at the point \( (0, 0, 3) \) and parallel to the \( X-Y \) plane, oriented so that the top of \( S \) points in the direction of the negative \( Z \)-axis. Compute \(\iint_{S} \vec{F} \cdot d\vec{r}\) where
\[
\vec{F}(x, y, z) = \begin{pmatrix} x + \sin(y) \\ z^3 - xyz \\ z + y - 1 \end{pmatrix}.
\]
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