Edexcel Mathematics Sample paper · Paper 1 · Question 14 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

Sample paper · Paper 1 · Question 14 · 10 marks

14. y C S O 1 x 3 Figure 4 Figure 4 shows a sketch of part of the curve C with equation y = 2 ln x x 3 − 2 x + 5, x > 0 The finite region S, shown shaded in Figure 4, is bounded by the curve C, the line with equation x = 1, the x-axis and the line with equation x = 3 The table below shows corresponding values of x and y with the values of y given to 4 decimal places as appropriate. x 1 y 3 1.5 2 2.5 3 2.3041 1.9242 1.9089 2.2958 (a) Use the trapezium rule, with all the values of y in the table, to obtain an estimate for the area of S, giving your answer to 3 decimal places. (3) (b) Explain how the trapezium rule could be used to obtain a more accurate estimate for the area of S. (1) (c) Show that the exact area of S can be written in the form a b are integers to be found. + ln c, where a, b and c (6) (In part c, solutions based entirely on graphical or numerical methods are not acceptable.)

Lesson: Locating Roots by Change of Sign