A flight computer calculates the total distance traveled by an autonomous drone by applying the trapezium rule to velocity data v(t)v(t)v(t) sampled over the interval 1≤t≤51 \le t \le 51≤t≤5. The computer evaluates four different mathematical models for the drone's velocity:
Model A: v(t)=3t+4v(t) = 3t + 4v(t)=3t+4
Model B: v(t)=12ln(t)v(t) = 12\ln(t)v(t)=12ln(t)
Model C: v(t)=12et/2v(t) = \frac{1}{2}e^{t/2}v(t)=21et/2
Model D: v(t)=10+4t−t2v(t) = 10 + 4t - t^2v(t)=10+4t−t2
Identify which model will result in the trapezium rule producing an overestimate of the actual distance traveled. Justify your answer.
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.