A subaquatic probe is descending into an ocean trench. Its rate of descent, v m min−1v\text{ m min}^{-1}v m min−1, is monitored over a 50-minute period. The following velocity readings were extracted from the probe's telemetry system at 10-minute intervals:
| t (min)t \text{ (min)}t (min) | 0 | 10 | 20 | 30 | 40 | 50 |
|---|---|---|---|---|---|---|
| v (m min−1)v \text{ (m min}^{-1})v (m min−1) | 15.0 | 42.4 | 58.6 | 55.2 | 39.8 | 12.5 |
An oceanographer, Marcus, claims that in the period 10≤t≤4010 \le t \le 4010≤t≤40, the probe descends approximately 1550 metres.
Determine whether Marcus is correct, showing clearly the calculations you have used based on the trapezium rule with all available data for this interval.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
