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The iterated integrals use spherical coordinates. Describe the solids determined by the limits of integration.

π2π02π02fρ,θ,ϕρ2sinϕdρdθdϕ

Short Answer

Expert verified

The region represents sphere with second quadrant with the hemisphere below the xy-plane of the sphere with radius 2 centered at origin

Step by step solution

01

Step 1:Given information

The given expression isπ2π02π02fρ,θ,ϕρ2sinϕdρdθdϕ

02

Step 2:Simplification

According to the order of integration

ρ=0toρ=2

width="141">x2+y2+z2=2

x2+y2+z2=22

This is a sphere equation

θvaries from θ=0toθ=2π

It means it is in the second quadrant

localid="1652082534348" ϕvaries fromπ2toπthese the region represents the hemisphere below the xy -plane of the sphere with radius 2 centered at the origin

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