1. The problem statement, all variables and given/known data Consider a vector A = (2x-y)i + (yz^2)j + (y^2z)k. S is a flat surface area of a rectangle bounded by the lines x = +-1 and y = +-2 and C is its rectangular boundary in the x-y plane. Determine the line integral ∫A.dr and its surface integral ∫(∇xA).n dS 2. Relevant equations 3. The attempt at a solution First I found ∇xA, which ended up simplifying to 1k so ∫k.n dS at this part I'm confused as to how to simplify it further. For the line integral, ∫A.dr =∫(2x-y)dx + ∫(yz^2)dy + ∫(y^2z)dz this is as far as i was able to understand, I'm not quite sure how to break up the integrals or what intervals to use. But for this line integral, I still tried =∫(2x-y)dx of side #1 + ∫(2x-y)dx of side #2 + .... of side #3 + .... of side #4 the 2nd and 4th sides I got were 0 since the change of dx was 0 =∫(2x+2)dx (from -1 to 1) - ∫(2x -2)dx (from -1 to 1) =8 not sure if this is a correct procedure at all, but I got an answer out of it. My problem with these questions is coming up with the integrals to solve, I'm sort of lost in how to determine them.