The velocity v(t)v(t)v(t) of a remote-controlled rover on a research mission, measured in m/s\text{m/s}m/s, is modeled by the function v(t)=10t2+5\displaystyle v(t) = \frac{10}{\sqrt{t^2+5}}v(t)=t2+510 for 2≤t≤42 \le t \le 42≤t≤4, where t t\,t is the time in seconds after activation. A technician records the rover's velocity at regular intervals as shown in the table below.
| ttt | 2 | 2.5 | 3 | 3.5 | 4 |
|---|---|---|---|---|---|
| v(t)v(t)v(t) | 3.33333 | 2.98142 | 2.67261 | 2.40772 | 2.18218 |
Use the trapezium rule with all the values in the table to find an approximate value for the total distance traveled by the rover between t=2t=2t=2 and t=4t=4t=4. Give your answer to four decimal places.
Using your answer to part (a), deduce an estimate for ∫2430t2+5 dt\displaystyle \int_{2}^{4} \frac{30}{\sqrt{t^2+5}} \, dt∫24t2+530dt.
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.
