G.3) Area and volume measurements via the Gauss-Green formula* This problem has lots of overlap with some of the work in the lesson on transformations of integrals. The Gauss-Green formula says Jfoxn[x, y] - dym[x, y] dxdy = [, m[x[t], y[t]] x'[t] + n[x[t], y[t]] y'[t] dt provided that {x[t], y[t]) sweeps out the boundary of the region R exactly one time in the counterclockwise fashion as t advances from a to b. If you take m[x, y] = y and n[x, y] = 0 and plug into the Gauss-Green formula, then you get -Sfoldxdy = SSR(0 - 1)dxdy = S' (y[t ] x '[t] + 0y'[t]) dt = [ y[t] x'[t] dt. Consequently, S y [t] x'[t ] dt measures the area of R provided that {x[t], y[t]) sweeps out the boundary of R exactly one time in the counterclockwise fashion as t advances from a to b. O G.3.a.i) Adapt the discussion above to explain why ['x[t] y'[t] dt also measures the area of R provided that {x[t], y[t]) sweeps out the boundary of R exactly one time in the counterclockwise fashion as t advances from a to b