The cross section of a scale model of a hill is modelled by the following graph. 10 8 6 4 2 0 0 10 20 30 x 40 The heights of the model are measured at horizontal intervals and are given in the table. Horizontal distance, xcm 0 10 20 30 40 Vertical distance, ycm 0 3 8 9 0 (a) Use the trapezoidal rule with $h = 10$ to find an approximation for the cross-sectional area of the model. It is given that the equation of the curve is $y = 0.04x^2 - 0.001x^3$, $0 le x le 40$. (b) (i) Write down an integral to find the exact cross-sectional area. (ii) Calculate the value of the cross-sectional area to two decimal places. (c) Find the percentage error in the area found using the trapezoidal rule.
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The points given are (0, 10), (10, 8), (20, 9), (30, 4), (40, 2), and (50, 0). You've already calculated the area using the trapezoidal rule to be 200 square cm in part (a). Show more…
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