Evaluate the following integral in spherical coordinates. SS Se- (x² + y² +2²) ² D 3/2 0 dV; D is a ball of radius 7 Set up the triple integral using spherical coordinates that should be used to evaluate the given integral as efficiently as possible. Use increasing limits of integration. 2π π 7 MPY. SS S 2 (343 -1) e-343 3 00 C... dp de de
Evaluate the following integral in spherical coordinates. SS Se- (x² + y² +2²) ² D 3/2 0 dV; D is a ball of radius 7 Set up the triple integral using spherical coordinates that should be used to evaluate the given integral as efficiently as possible. Use increasing limits of integration. 2π π 7 MPY. SS S 2 (343 -1) e-343 3 00 C... dp de de
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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I ended up getting this answer, but it is wrong. One other thing I'm confused about is how the bounds can be acquired mathematically without looking at a visual graph. Can you explain this?
![**Evaluating Integrals in Spherical Coordinates**
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Evaluate the following integral in spherical coordinates.
\[
\iiint_D e^{-\left(x^2 + y^2 + z^2\right)^{3/2}} \, dV; \quad D \text{ is a ball of radius } 7
\]
---
Set up the triple integral using spherical coordinates that should be used to evaluate the given integral as efficiently as possible. Use increasing limits of integration.
\[
\int_0^{2\pi} \int_0^{\pi} \int_0^7 2\left(e^{343} - 1\right) e^{-343} \frac{\rho^2 \sin\phi}{3} \, d\rho \, d\phi \, d\theta
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ae96ba-8296-4f48-84d9-a65ba8f4727e%2F2ca94d14-89fd-41d5-b6ce-3772f0101c9f%2F336jnk7_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluating Integrals in Spherical Coordinates**
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Evaluate the following integral in spherical coordinates.
\[
\iiint_D e^{-\left(x^2 + y^2 + z^2\right)^{3/2}} \, dV; \quad D \text{ is a ball of radius } 7
\]
---
Set up the triple integral using spherical coordinates that should be used to evaluate the given integral as efficiently as possible. Use increasing limits of integration.
\[
\int_0^{2\pi} \int_0^{\pi} \int_0^7 2\left(e^{343} - 1\right) e^{-343} \frac{\rho^2 \sin\phi}{3} \, d\rho \, d\phi \, d\theta
\]
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