1. Find 0/22cos2xcosxdx (Hint: Use the identity sin2x+cos2x=1 ) (10 marks) 2. Figure 1 shows a sketch of part of the curve with equation y=x21ln2x. The finite region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and the lines x =1 and x=4. Figure 1 (a) Use trapezium rule, with 3 strips of equal width, to find an estimate for the area of R, giving your answer to 2 decimal places. (5 marks) (b) Find x21ln2xdx (5 marks) (c) Hence find the exact area of R, giving your answer in the form aln2+b, where a and b are exact constants