(a) Express the triple integral ||/ f (x, y, z, ) dVas an iterated integral in spherical coordinates for the E given function f and solid region E. (b) Evaluate the iterated integral. 21. f(x, y, z) = Vx² + y² + z² + y² + z² = 4 x² + y² +z? = 9

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**(a)** Express the triple integral \(\iiint_E f(x, y, z) \, dV\) as an iterated integral in spherical coordinates for the given function \(f\) and solid region \(E\).

**(b)** Evaluate the iterated integral.

**21.** \(f(x, y, z) = \sqrt{x^2 + y^2 + z^2}\)

The accompanying diagram features a 3D coordinate system with axes labeled \(x\), \(y\), and \(z\). Two spherical surfaces are depicted:

- The outer surface is labeled \(x^2 + y^2 + z^2 = 4\).
- The inner surface is labeled \(x^2 + y^2 + z^2 = 9\).

The region \(E\) is shaded between these surfaces, indicating the volume for which the integral is evaluated.
Transcribed Image Text:**(a)** Express the triple integral \(\iiint_E f(x, y, z) \, dV\) as an iterated integral in spherical coordinates for the given function \(f\) and solid region \(E\). **(b)** Evaluate the iterated integral. **21.** \(f(x, y, z) = \sqrt{x^2 + y^2 + z^2}\) The accompanying diagram features a 3D coordinate system with axes labeled \(x\), \(y\), and \(z\). Two spherical surfaces are depicted: - The outer surface is labeled \(x^2 + y^2 + z^2 = 4\). - The inner surface is labeled \(x^2 + y^2 + z^2 = 9\). The region \(E\) is shaded between these surfaces, indicating the volume for which the integral is evaluated.
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