This problem uses the result you studied in Lab 7on differentiating the circulation of a fieldabout a point:IfClonis a family of simple closed curves shrinking to a point (a,b)in its interior aslon0, thenlimlon01areaenclosedbyClonoClonF*dr=Qx(a,b)-Py(a,b)Let Dbe a domain asin the figure below, and F=(:P,Q:)an arbitrary smooth field. Let usthink about the integral of the circulation density:D(Qx-Py)dALet us approximate this integral by a Riemann ??S associated to the shown partition (givenby the graph paper), and the midpoint rule.Figure 1:Pick a sub-rectangle (square)Rijin the subdivision of the domain D. Let (xi*,yj*)be itsmidpoint, and its sides x,y. Using your conjecture, approximate(Qx-Py)(x*,y*)xyby a circulation. What is the corresponding loop?(a) The Riemann ??Sis the sum of the numbers (Qx-Py)(xi*,yj*)xy over all thesubrectangles R.Using what you learned in Lab 7, what is the sum of the circulations of part (1) overall the subrectangles?Hint: Think of two adjacent subrectangles, asin problem 2of homework 9:(b) How does your previous answer support the statement of Green's theorem?