2. Figure 1 shows a sketch of part of the curve with equation \( y=x^{\frac{1}{2}} \ln 2 x \). The finite region R, shown shaded in Figure 3, is bounded by the curve, the \( x \)-axis and the lines \( x \) \( =1 \) and \( \mathrm{x}=4 \). 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 \( \int x^{\frac{1}{2}} \ln 2 x d x \) (5 marks) (c) Hence find the exact area of \( R \), giving your answer in the form \( a \ln 2+b \), where \( \mathrm{a} \) and \( \mathrm{b} \) are exact constants. (5 marks)