**??? - 2014 q3**

3.

Fig. 3 shows the curve

Fig. 3 shows the curve

*y*=

*x*

^{3}+ √(sin

*x*), 0≤

*x*≤ π/4

(i) Use the trapezium rule with 4 strips to estimate the area of the region bounded by the curve, the

(ii) Suppose the number of strips in the trapezium rule is increased. Without doing further calculations, state, with a reason, whether the area estimate increases, decreases, or it is not possible to say. [1]

*x*-axis and the line*x*=π/4 , giving your answer to 3 decimal places. [4](ii) Suppose the number of strips in the trapezium rule is increased. Without doing further calculations, state, with a reason, whether the area estimate increases, decreases, or it is not possible to say. [1]