# How do you integrate int 3 dt?

Feb 26, 2017

$3 t + C .$

#### Explanation:

We know that, for a const. $k , \int k f \left(t\right) \mathrm{dt} = k \int f \left(t\right) \mathrm{dt} .$

$\therefore \int 3 \mathrm{dt} = 3 \int \mathrm{dt} = 3 \int {t}^{0} \mathrm{dt} .$

Since, $\int {t}^{n} \mathrm{dt} = {t}^{n + 1} / \left(n + 1\right) + c , w h e r e , n \ne - 1 ,$ we have,

$\int 3 \mathrm{dt} = 3 \int {t}^{0} \mathrm{dt} = 3 \left\{{t}^{0 + 1} / \left(0 + 1\right)\right\} = 3 \left({t}^{1} / 1\right) = 3 t + C .$