12 5. The curve C has equation y = arccos  1 2 x                −2  x  2 (a) Show that C has no stationary points. (3) The normal to C, at the point where x = 1 , crosses the x-axis at the point A and crosses the y-axis at the point B. Given that O is the origin, (b) show that the area of the triangle OAB is 1 54 (p 3 + qπ + r 3 π2)  where p, q and r are integers to be determined. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________