$($a$)$ Suppose that the acceleration function of a particle moving along a coordinate line is $a(t)=t+1.$ Find the average acceleration of the particle over the time interval $0t2$ by integrating.

$a_{\text{a}\text{v}\text{e}}=$

$($b$)$ Suppose that the velocity function of a particle moving along a coordinate line is $v(t)=6cos(t).$ Find the average acceleration of the particle over the time interval $0t\frac{}{4}$ algebraically.

$a_{\text{a}\text{v}\text{e}}=$