# How do you evaluate the definite integral int(2x+2)dx from [-3,1]?

Dec 15, 2016

$0$

#### Explanation:

Integrate each term using the $\textcolor{b l u e}{\text{power rule for integration}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\int a {x}^{n} \mathrm{dx} = \frac{a}{n + 1} {x}^{n + 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow {\int}_{-} {3}^{1} \left(2 x + 2\right) \mathrm{dx} = {\left[{x}^{2} + 2 x\right]}_{-} {3}^{1}$

Now, subtract the evaluation of the lower limit from the evaluation of the upper limit.

$\Rightarrow \left(1 + 2\right) - \left(9 - 6\right) = 3 - 3 = 0$