Solution verification of flux integral $\iint_DF\cdot\hat{n}dS$ with $F=(2x,y,z)$

65 Views Asked by At

Compute the flux of $F=(2x,y,z)$ through the surface $$ r = u^2v\,\hat{\imath} + uv^2\,\hat{\jmath} + v^3\,\hat{k}, \quad 0\leq u \leq 1, \quad 0 \leq v \leq 1 $$

My approach: is it correct?enter image description here