Given a function G(r) with cylindrical symmetry show the following 17. (eylindrical surface G(r)da = 2 L r G(r)+ 4 G(r) r dr radius R length "L" %3D cylindrical surface radius R length_"L" G(r)dV = 2 1 L G(r) r dr 18.
Given a function G(r) with cylindrical symmetry show the following 17. (eylindrical surface G(r)da = 2 L r G(r)+ 4 G(r) r dr radius R length "L" %3D cylindrical surface radius R length_"L" G(r)dV = 2 1 L G(r) r dr 18.
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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Question
![Given a function \( G(r) \) with cylindrical symmetry, show the following:
17.
\[
\int_{\text{cylindrical surface}}^{\text{radius } R, \text{ length } "L"} G(r) \, da = 2 \cdot \pi \cdot L \cdot r \cdot G(r) + 4 \cdot \pi \int_0^R G(r) \cdot r \cdot dr
\]
18.
\[
\int_{\text{cylindrical surface}}^{\text{radius } R, \text{ length } "L"} G(r) \, dV = 2 \cdot \pi \cdot L \int_0^R G(r) \cdot r \cdot dr
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa06fb91f-1445-4bd6-b9dd-268642fc0d22%2Fcb1dbaf8-36fe-4e9c-b6d7-c009a599e3d6%2Fhao6by9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a function \( G(r) \) with cylindrical symmetry, show the following:
17.
\[
\int_{\text{cylindrical surface}}^{\text{radius } R, \text{ length } "L"} G(r) \, da = 2 \cdot \pi \cdot L \cdot r \cdot G(r) + 4 \cdot \pi \int_0^R G(r) \cdot r \cdot dr
\]
18.
\[
\int_{\text{cylindrical surface}}^{\text{radius } R, \text{ length } "L"} G(r) \, dV = 2 \cdot \pi \cdot L \int_0^R G(r) \cdot r \cdot dr
\]
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