Turn over 33  Question 10 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 10 is 8 marks) 34   11. y R O x 2 4 Figure 2 Figure 2 shows a sketch of part of the curve with equation y = (ln x) 2        x > 0 The finite region R, shown shaded in Figure 2, is bounded by the curve, the line with equation x = 2, the x-axis and the line with equation x = 4 The table below shows corresponding values of x and y, with the values of y given to 4 decimal places. x 2 2.5 3 3.5 4 y 0.4805 0.8396 1.2069 1.5694 1.9218 (a) Use the trapezium rule, with all the values of y in the table, to obtain an estimate for the area of R, giving your answer to 3 significant figures. (3) (b) Use algebraic integration to find the exact area of R, giving your answer in the form y = a (ln 2) 2 + b ln 2 + c where a, b and c are integers to be found. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________