Please answer all the questions, so I can check it with what I handed in. Thank you

Question 5 (16 marks) a. Consider (from Question 2) the polynomial function g(x) = x -x3. i. Sketch the function again showing the intercepts with the axes and shade the region enclosed by the function and the positive x axis. (1 mark) ii. Determine the area of the shaded region. (4 marks) iii. Show that the volume of the solid created when the shaded region is rotated around the x axis is 37 105 cubic units. Hint: Consider a slice through the solid (4 marks) perpendicular to the x axis. b. Consider the system of equations: X1 + X2 + X3 = 18 2x1+ X2 - X3 = 3 3x1 + 2x2 - X3 = 12 i. Write the system in the form Ax = b . (1 mark) ii. Calculate the inverse of A using the Gauss-Jordan method. (4 marks) iii. Using the inverse of A, find the solution X = X 2 X 3 (2 marks)