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## Homework Statement

Compute the flux of a vector field ##\vec{v}## through the unit sphere, where

$$ \vec{v} = 3xy i + x z^2 j + y^3 k $$

## Homework Equations

Gauss Law:

$$ \int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$

## The Attempt at a Solution

Ok so after applying Gauss Law, one gets

$$ \int 3y dV $$

and after converting it into a spherical integral I get

$$3 \int_0^{ \pi} \sin^2 \theta d \theta \int_0^{2 \pi} \sin \phi d \phi = 0$$ since integral of sin over a full period is. Is this correct? or if not, where did I go wrong?