**??? - 2016 Q2**

2.

Figure 1 shows a sketch of part of the curve with equation

The finite region R, shown shaded in Figure 1, is bounded by the curve, the

*y*=*x*^{2}ln*x*, x≥1The finite region R, shown shaded in Figure 1, is bounded by the curve, the

*x*-axis and the line*x*= 2 The table below shows corresponding values of*x*and*y*for*y*=*x*^{2}ln*x* (a) Complete the table above, giving the missing value of

(b) Use the trapezium rule with all the values of

(c) Use integration to find the exact value for the area of

*y*to 4 decimal places. (1)(b) Use the trapezium rule with all the values of

*y*in the completed table to obtain an estimate for the area of*R*, giving your answer to 3 decimal places. (3)(c) Use integration to find the exact value for the area of

*R*. (5)