# How do you evaluate the definite integral int (-3v+4)dv from [2,5]?

May 23, 2018

$- \frac{39}{2}$

#### Explanation:

${\int}_{2}^{5} \left(- 3 v + 4\right) \mathrm{dv}$

the antiderivative is $F \left(v\right) = - \frac{3}{2} {v}^{2} + 4 v$

simply evaluate $F \left(5\right) - F \left(2\right)$
$= - \frac{3}{2} {\left(5\right)}^{2} + 4 \left(5\right) + \frac{3}{2} {\left(2\right)}^{2} - 4 \left(2\right)$
$= - \frac{75}{2} + 20 + 6 - 8$
$= - \frac{39}{2}$