During a test flight of a high-performance drone, the power consumption rate PPP (in kW) is monitored over a 2-minute interval. The rate at time t t\,t minutes is modelled by the function:
P=2.5t2t2+5 P = \frac{2.5^t}{\sqrt{2t^2 + 5}} P=2t2+52.5tComplete the table below, giving the values of PPP to 3 decimal places.
| ttt | 0 | 0.5 | 1 | 1.5 | 2 |
|---|---|---|---|---|---|
| PPP | 0.447 | 0.945 | 1.733 |
Use the trapezium rule, with all the values of PPP from the completed table, to find an approximate value for the total energy consumed over the interval:
∫022.5t2t2+5 dt \int_{0}^{2} \frac{2.5^t}{\sqrt{2t^2 + 5}} \, dt ∫022t2+52.5tdt
