Answer
16.5
Work Step by Step
Use the table
Basic Integration Rules, p.246
$F(\displaystyle \mathrm{t})=7t-\frac{3}{2}t^{2}$
$F^{\prime}(t)=7-3t=f(t), $
so, by the Fundamental Theorem of Calculus,
$\displaystyle \int_{-1}^{2}(7-3t)dt=F(2)-F(-1)$
$=[7t-\displaystyle \frac{3}{2}t^{2}]_{-1}^{2}$
$=[7(2)-\displaystyle \frac{3}{2}(4)]-[7(-1)-\frac{3}{2}(-1)^{2}]$
$=14-6+7+\displaystyle \frac{3}{2}$
$=\displaystyle \frac{33}{2}=16.5$
See below: work done in desmos.com -
The trapezoid has bases 1 and 10, height 3,
$A=\displaystyle \frac{1+10}{2}\cdot 3=16.5$
