The rate fuel is consumed by an aircraft is given by$\displaystyle f(a,s)=10+a+\frac{s^2}{2}$ where $\displaystyle a$ is its forward acceleration and $\displaystyle s$ is its vertical acceleration. How much fuel did the aircraft consume over time interval $\displaystyle [0,2]$ if $\displaystyle (a,s)$ are given by the following parameterized curve:

$\displaystyle a(t)=\{{t }$, $\displaystyle t\in [0,1]$ and $\displaystyle 2-t$,$\displaystyle t\in (1,2]$

AND

$\displaystyle s(t)=\{2$, $\displaystyle t\in[0,1]$ and $\displaystyle 1$,$\displaystyle t\in(1,2]$