Question

Find the flux of the vector field F(x, y, z) = zi + yj + xk across
the unit sphere x^2 + y^2 + z^2 = 1.

please help me im so lost

Answer 1

help!!!!! please please please please im going crazy

Answer 2

\[\vec{F}(x,y,z)=z\vec{i}+y\vec{j}+x\vec{k}\quad,\quad S:x^2+y^2+y^2=1\]\[\oint\limits_S\vec{F}\cdot d\vec{S}=\iiint\limits_V \underbrace{div\vec{F}}_{=1}\,\,dv=V=\frac{4\pi}{3}\]