An experimental physicist is using the trapezium rule to estimate the total impulse (the area under a force-time graph) for four different test engines over the interval 0≤t≤50 \le t \le 50≤t≤5. The force F(t)F(t)F(t) (in Newtons) for each engine is modeled by the following functions:
Engine A: F(t)=1.5t+20F(t) = 1.5t + 20F(t)=1.5t+20 Engine B: F(t)=0.4t2+10F(t) = 0.4t^2 + 10F(t)=0.4t2+10 Engine C: F(t)=6t+4F(t) = 6\sqrt{t+4}F(t)=6t+4 Engine D: F(t)=60t+3\displaystyle F(t) = \frac{60}{t+3}F(t)=t+360
Identify the engine model for which the trapezium rule will produce an underestimate of the actual impulse over this interval. Justify your answer by considering the concavity of the models.
