11 Fig. 11 shows the cross-section of a school hall, with measurements of the height in metres taken at 1.5 m intervals from O .
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\caption{Fig. 11}
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- Use the trapezium rule with 8 strips to calculate an estimate of the area of the cross-section.
- Use 8 rectangles to calculate a lower bound for the area of the cross-section.
The curve of the roof may be modelled by \(y = - 0.013 x ^ { 3 } + 0.16 x ^ { 2 } - 0.082 x + 2.4\), where \(x\) metres is the horizontal distance from O across the hall, and \(y\) metres is the height.
- Use integration to find the area of the cross-section according to this model.
- Comment on the accuracy of this model for the height of the hall when \(x = 7.5\).