Set up the integral for I = ||| x² + y² + 2² dV over the region R R described by Vr2 + y² > 1, Vr² + y² + z² < 2 (a bead-shaped region, see Figure 1) in the specified coordinate system. Do not evaluate the integrals. (a) Cylindrical coordinates, order of integration dz dr do. (b) Cylindrical coordinates, order of integration dr dz dO. (c) Spherical coordinates. 56 Evaluate the integral in 1(b). You should get I = 3T.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I need help with the following questions in the image.

Set up the integral for I =
II 2 + y? + 2? dV over the region R
R
described by Vr? + y? > 1, Vr² + y² + z² < 2 (a bead-shaped
region, see Figure 1) in the specified coordinate system. Do not
evaluate the integrals.
(a) Cylindrical coordinates, order of integration dz dr dø.
(b) Cylindrical coordinates, order of integration dr dz do.
(c) Spherical coordinates.
56
Evaluate the integral in 1(b). You should get I =
V3T.
5
Transcribed Image Text:Set up the integral for I = II 2 + y? + 2? dV over the region R R described by Vr? + y? > 1, Vr² + y² + z² < 2 (a bead-shaped region, see Figure 1) in the specified coordinate system. Do not evaluate the integrals. (a) Cylindrical coordinates, order of integration dz dr dø. (b) Cylindrical coordinates, order of integration dr dz do. (c) Spherical coordinates. 56 Evaluate the integral in 1(b). You should get I = V3T. 5
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