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(a) Calculate the volume integral of f(r,0, z) r2³ sin over the half cylinder seated at the origin, with radius r = 1 and height 4 along the z-axis, with 0≤z≤4, 0≤0 ≤ T.

(a) Calculate the volume integral of f(r,0, z) r2³ sin over the half cylinder seated at the origin, with radius r = 1 and height 4 along the z-axis, with 0≤z≤4, 0≤0 ≤ T.

Advanced Engineering Mathematics
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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(a) Calculate the volume integral of f(r,0, z) = r2³ sin over the half cylinder seated at the origin, with radius r = 1 and height 4 along the z-axis, with 0≤z≤4, 0≤0ST. (b) Calculate the mass of a sphere of radius 3 centred at the origin, and with density function f(r,0,0)=r0 cos² (6), where 0 <r<3, 0≤0≤2, 0≤ ≤n.
Transcribed Image Text:(a) Calculate the volume integral of f(r,0, z) = r2³ sin over the half cylinder seated at the origin, with radius r = 1 and height 4 along the z-axis, with 0≤z≤4, 0≤0ST. (b) Calculate the mass of a sphere of radius 3 centred at the origin, and with density function f(r,0,0)=r0 cos² (6), where 0 <r<3, 0≤0≤2, 0≤ ≤n.
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