IB Maths AI SL AI 5.2 Integration and kinematics questions

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Question 1

Paper 1Medium6 marks

A surveyor estimates the area of an irregular lake inlet. A straight survey line of length $220\text{ m}$ is laid along one edge of the inlet. At equally spaced stations, the perpendicular distance from the line to the opposite shoreline is measured. The width increases continuously between consecutive stations.

Distance along survey line (m)	0	55	110	165	220
Width (m)	0	15	28	42	55

(a)

Use the trapezoidal rule to estimate the area of the inlet. Give your answer to the nearest $10\text{ m}^2$

[3]

(b)

Use rectangular strips to find lower and upper estimates for the area. Hence state bounds for the true area and whether your estimate in part (a) is consistent with these bounds.

[3]

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