1 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.
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\caption{Fig. 12}
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- Use the trapezium rule with 5 strips to estimate the area of the end wall of the building.
- Oskar now uses the equation \(y = - 0.001 x ^ { 3 } - 0.025 x ^ { 2 } + 0.6 x + 9\), for \(0 \leqslant x \leqslant 15\), 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.
(B) Use integration to find the area of the end wall given by this model.