Answered: Use spherical coordinates. Evaluate y²…

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Calculus

Use spherical coordinates. Evaluate y² dv, where E is the solid hemisphere x² + y² + z² ≤ 4, y ≥ 0. E

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Question

Use spherical coordinates.
Evaluate
y² dv, where E is the solid hemisphere x² + y² + z² ≤ 4, y ≥ 0.

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Step 2: Using spherical coordinates

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Step 3: Using Double, Triple angle formula

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Step 4: Integrating

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