**??? - 2014 JUNE Q12**

Oskar is designing a building. Fig. 12 shows his design for the end wall and the curve of the roof. The units
for

*x*and*y*are metres.(i) Use the trapezium rule with 5 strips to estimate the area of the end wall of the building. [4]

(ii) Oskar now uses the equation

(A) Calculate the difference between the height of the roof when

(B) Use integration to find the area of the end wall given by this model. [4]

(ii) Oskar now uses the equation

*y*= -0.001*x*^{3}- 0.025*x*^{2}+ 0.6*x*+ 9, for 0 ≤*x*≤ 15 to model the curve of the roof.(A) Calculate the difference between the height of the roof when

*x*= 12 given by this model and the data shown in Fig. 12. [2](B) Use integration to find the area of the end wall given by this model. [4]