Question 3: [40 marks] Calculate the total charge Q of a thin plate with the charge density distribution p (x, y) = x y mC/m-. The plate shape is restricted by the lines: y = 2 - x and y = 2x - 1, where x and y are measured in metres. a) Sketch the plate shape. [10 marks] b) Present the total charge through the double integral. [4 marks] c) Reduce the double integral to the repeated integrals and show limits of integration. [6 marks] d) Calculate the integral and present your answer with five significant figures. [20 marks] Rubric: 2 marks if the upper boundary of the domain of integration is plotted correctly; 2 marks if the lower boundary of the domain of integration is plotted correctly; 6 marks if the points of intersection are found correctly; 4 marks if the total charge correctly presented through the double integral; 6 marks if the double integral is reduced to the repeated integrals correctly