Evaluate $\iint_{S}\vec{A}.\vec{n} ds$ ,where $ \vec{A}= (x+y^2) \hat{i} -2x\hat{j} + 2yz \hat{k} $ and S is the surface of the plane 2x+ y +2z =6 in the first octant.
Where I stand :
I have tried to do this problem but couldn't go far as I was unable to find the differential area. My friend shared an interesting idea that what we essentially calculate is the flux and flux through the axis planes should be the flux through surface. I agreed, but She calculated it for only the xy plane (which matches the answer in the book) But shouldn't we also calculate the flux contributed by the other two surfaces (yz ,zx)? I will share the solution given by my friend. My friend's Soln.
