Question
Asked Nov 24, 2019
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Use geometry to evaluate ∫∫∫1 dV where R is the region inside the sphere x2+y2+z2=4.

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Expert Answer

Step 1

Given R as the region inside the sphere

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x2 y 4 To evaluate: ff 1dV

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Step 2

Since the given geometric region is the region inside of a sphere, we use the spherical coordinate.

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In spherical coordinates, the sphere is all points where 0 Ø<T(the angle measured down from the positive z axis ranges), 0 < 0 < 2x (like polar coordinates), and 0 ps 2

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Step 3

And we get a vo...

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2TT 2 TT p2 sin(Ø) dpdedø 1dV 2TT 2 TT p2dp sin(ø)dø de (2)(2m) 2 32 Tt cu. units 3

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Tagged in

Math

Calculus