Consider the triple integral JJJ (x+y+z)dV E where E is the solid enclosed by the cylinder x² + y² = 4, the sphere x²+y²+z² = 25, and the plane z = 0. a. Sketch the solid E in the xyz-plane. = b. Setup the iterated triple integral in Cartesian coordinate system using dA dzdxdy and dA = dydzdx.

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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Consider the triple integral
!!!
(x+y+z)dV
E
where E is the solid enclosed by the cylinder x² + y² = 4, the sphere x²+y²+z² = 25,
and the plane z = 0.
a. Sketch the solid E in the xyz-plane.
=
b. Setup the iterated triple integral in Cartesian coordinate system using dA
dzdxdy and dA = dydzdx.
c. Setup the iterated triple integral in cylindrical coordinate system where dV =
rdzdrd0.
d. Setup the iterated triple integral in spherical coordinate system.
Transcribed Image Text:Consider the triple integral !!! (x+y+z)dV E where E is the solid enclosed by the cylinder x² + y² = 4, the sphere x²+y²+z² = 25, and the plane z = 0. a. Sketch the solid E in the xyz-plane. = b. Setup the iterated triple integral in Cartesian coordinate system using dA dzdxdy and dA = dydzdx. c. Setup the iterated triple integral in cylindrical coordinate system where dV = rdzdrd0. d. Setup the iterated triple integral in spherical coordinate system.
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