Evaluate e y2z2 dv, where e lies above the cone ϕ = π/3 and below the sphere ρ = 1.

The volume of the solid using the triple integral

Given that;

Then the spherical coordinates can be expressed as:

where;

Now, the expression for the solid E in the spherical coordinates can be computed as:

and the volume of the solid using the triple integral is calculated as:

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In spherical coordinates, we set

so that the volume element under this transformation becomes

The region is given by the set

so that the integral is

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