Question 5 A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere attached on top of the cylinder, as shown in the figure below. Figure Q5 (a) The projection of solid E onto the yz-plane can be described as follows: Projection of E onto yz-plane = {(y, z)|– 3< y< 3,0 < z< 4 + /9 - (1) Describe the projection of solid E onto the xy- and xz-plane. (ii) Describe solid E. (b) (i) Consider the integration over the solid domain E x dV. Rewrite this integration as an iterated integral with dz first, followed by dy, then dx. (ii) Rewrite the iterated integral in Question 5(b) (i) by converting to cylindrical coordinates. (iii) Hence, compute the integral.
Question 5 A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere attached on top of the cylinder, as shown in the figure below. Figure Q5 (a) The projection of solid E onto the yz-plane can be described as follows: Projection of E onto yz-plane = {(y, z)|– 3< y< 3,0 < z< 4 + /9 - (1) Describe the projection of solid E onto the xy- and xz-plane. (ii) Describe solid E. (b) (i) Consider the integration over the solid domain E x dV. Rewrite this integration as an iterated integral with dz first, followed by dy, then dx. (ii) Rewrite the iterated integral in Question 5(b) (i) by converting to cylindrical coordinates. (iii) Hence, compute the integral.
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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Transcribed Image Text:Question 5
A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere
attached on top of the cylinder, as shown in the figure below.
Figure Q5
(a)
The projection of solid E onto the yz-plane can be described as follows:
Projection of E onto yz-plane = {(y, z) |– 3<y< 3,0 <z<4+ /9 -
– y²} .
(i)
Describe the projection of solid E onto the xy- and xz-plane.
(ii)
Describe solid E.
(b)
(i)
Consider the integration over the solid domain E
x dV.
Rewrite this integration as an iterated integral with dz first, followed by dy,
then dx.
(ii)
Rewrite the iterated integral in Question 5(b) (i) by converting to cylindrical
coordinates.
(iii)
Hence, compute the integral.
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