Verify the Divergence Theorem for the vector field and region: F = (7x, 92, 9y) and the region x² + y² ≤ 1, 0≤x≤8 Sfs F. ds = SSSR div(F) dv =
Verify the Divergence Theorem for the vector field and region: F = (7x, 92, 9y) and the region x² + y² ≤ 1, 0≤x≤8 Sfs F. ds = SSSR div(F) dv =
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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![**Verification of the Divergence Theorem**
**Given:**
Verify the Divergence Theorem for the following vector field and region:
\[ \mathbf{F} = \langle 7x, 9z, 9y \rangle \]
and the region defined by:
\[ x^2 + y^2 \leq 1, \]
\[ 0 \leq z \leq 8 \]
**Equations:**
1. Surface Integral:
\[
\iint_S \mathbf{F} \cdot d\mathbf{S} = \boxed{}
\]
2. Volume Integral:
\[
\iiint_R \text{div}(\mathbf{F}) \, dV = \boxed{}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49444d66-96b7-45b8-992f-0f6c51b0e4d0%2Fec8c6bb8-e731-4603-bf01-7da514c1c7e7%2Fxvnmw2p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Verification of the Divergence Theorem**
**Given:**
Verify the Divergence Theorem for the following vector field and region:
\[ \mathbf{F} = \langle 7x, 9z, 9y \rangle \]
and the region defined by:
\[ x^2 + y^2 \leq 1, \]
\[ 0 \leq z \leq 8 \]
**Equations:**
1. Surface Integral:
\[
\iint_S \mathbf{F} \cdot d\mathbf{S} = \boxed{}
\]
2. Volume Integral:
\[
\iiint_R \text{div}(\mathbf{F}) \, dV = \boxed{}
\]
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