Write a triple integral which computes the integral of the function f(x,y,z) = xz over the region R which is 1) inside the half-cylinder of radius 1/2 and centered at 0, x? + y2 = y, x20, 2) bounded below by the half-sphere z= /11-x - y2, 3) bounded above by the plane z = V11. Write this as a triple integral in cylindrical coordinates

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Write a triple integral which computes the integral of the function
f(x,y,z) = xz
over the region R which is
0.5: * +y? =y, x20,
1) inside the half-cylinder of radius 1/2 and centered at 0,
2) bounded below by the half-sphere z= V11-x² - y?,
3) bounded above by the plane z =
V11.
Write this as a triple integral in cylindrical coordinates
Transcribed Image Text:Write a triple integral which computes the integral of the function f(x,y,z) = xz over the region R which is 0.5: * +y? =y, x20, 1) inside the half-cylinder of radius 1/2 and centered at 0, 2) bounded below by the half-sphere z= V11-x² - y?, 3) bounded above by the plane z = V11. Write this as a triple integral in cylindrical coordinates
02 r2 z2
SS
dz dr de
01 r1 z1
01 =
02 =
r1 =
r2 =
z1 =
z2 =
Transcribed Image Text:02 r2 z2 SS dz dr de 01 r1 z1 01 = 02 = r1 = r2 = z1 = z2 =
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