Consider the solid that is bounded above by x² + y² + z? = 16 and below by z = Jx² + y². Set up only the appropriate triple integrals in rectangular, cylindrical, and spherical coordinates needed to find the volume of the solid.
Consider the solid that is bounded above by x² + y² + z? = 16 and below by z = Jx² + y². Set up only the appropriate triple integrals in rectangular, cylindrical, and spherical coordinates needed to find the volume of the solid.
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:Consider the solid that is bounded above by x² + y² + z? = 16 and below by z = Jx² + y². Set up only
the appropriate triple integrals in rectangular, cylindrical, and spherical coordinates needed to find the
volume of the solid.
Expert Solution
Step 1
Given:
The solid that is bounded above by x2+ y2+ z2=16 and below by
Step 2
To set up the triple integral in rectangular coordinate first solve the equation x2+y2+z2=16 for z, we get
The solid is bounded above the upper part of the sphere
Therefore, the volume of the solid in rectangular coordinate is
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