Gauβ's divergence theorem

int(S) (sin(x)dydz +(1-cos(x))ydzdx), S : x^2+y^2+z^2=1

=int(V) {∂ｘ（sin(x)）+∂ｙ（(1-cos(x))y）} dV, dV=dxdydz, V : x^2+y^2+z^2<=1

=int(V)dV

=4π/3