Evaluate the surface integral || F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi – yj + z³k, S is the part of the cone z = V x2 between the planes z = 1 and z = 2 with downward orientation
Evaluate the surface integral || F. ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi – yj + z³k, S is the part of the cone z = V x2 between the planes z = 1 and z = 2 with downward orientation
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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Please solve the screenshot. The answer is none of 109pi/15, -109pi/15, 209pi, or -209pi/15. Thanks.
![**Evaluate the Surface Integral**
Evaluate the surface integral
\[
\iint_S \mathbf{F} \cdot d\mathbf{S}
\]
for the given vector field **F** and the oriented surface **S**. In other words, find the flux of **F** across **S**. For closed surfaces, use the positive (outward) orientation.
**Vector Field:**
\[
\mathbf{F}(x, y, z) = -x\mathbf{i} - y\mathbf{j} + z^3\mathbf{k}
\]
**Surface:**
**S** is the part of the cone
\[
z = \sqrt{x^2 + y^2}
\]
between the planes \( z = 1 \) and \( z = 2 \) with downward orientation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56945fae-aeca-4f60-8c3d-a266c334f238%2F64ff4a2e-7dd1-45e6-8825-cb2218851173%2Ftaugd6_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the Surface Integral**
Evaluate the surface integral
\[
\iint_S \mathbf{F} \cdot d\mathbf{S}
\]
for the given vector field **F** and the oriented surface **S**. In other words, find the flux of **F** across **S**. For closed surfaces, use the positive (outward) orientation.
**Vector Field:**
\[
\mathbf{F}(x, y, z) = -x\mathbf{i} - y\mathbf{j} + z^3\mathbf{k}
\]
**Surface:**
**S** is the part of the cone
\[
z = \sqrt{x^2 + y^2}
\]
between the planes \( z = 1 \) and \( z = 2 \) with downward orientation.
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