Chapter 6, Problem 7RE

Fuel consumption A small plane in flight consumes fuel at a rate (in gal/min) given by

$R^{\prime }(t)=\{\begin{array}{ll}4t^{1/3}\hfill & \text{if}0\le t\le 8(\text{take-off})\hfill \\ 2\hfill & \text{if}t>8(\text{cruising}).\hfill \end{array}$

1. a. Find a function R that gives the total fuel consumed, for 0 ≤ t ≤ 8.
2. b. Find a function R that gives the total fuel consumed, for t ≥ 0.
3. c. If the fuel tank capacity is 150 gal, when does the fuel run out?