Consider the graph of f(x) = (x -2)3 + 1. a) Calculate the average value of the function over the interval x E [2, 5], showing all working. Give your answer in exact form. [3 marks] The graphs of f(x) = (x - 2)' + 1 and g(x) = (x - 3)2 - 1 are shown below. 8 6 + 4 P > X -2\fb) Find the points of intersection P and Q of these two graphs, using your calculator. Give the coordinates of point Q correct to 2 decimal places. [2 marks] c) Hence, using your answers from part b), write an integral to represent the area between the two curves. [1 mark] d) Using your integral from part c), nd this area using your calculator. Give your answer correct to 2 decimal places. [1 mark]