# How do you evaluate the definite integral int (3x^4)dx from [2,4]?

Mar 19, 2017

${\int}_{2}^{4} \left(3 {x}^{4}\right) \mathrm{dx} = \frac{2976}{5}$

#### Explanation:

${\int}_{2}^{4} \left(3 {x}^{4}\right) \mathrm{dx}$

$= {\left[\frac{3}{5} {x}^{5}\right]}_{2}^{4}$

$= \frac{3}{5} {\left(4\right)}^{5} - \frac{3}{5} {\left(2\right)}^{5}$

$= \frac{3}{5} \left({4}^{5} - {2}^{5}\right)$

$= \frac{3}{5} \left(1024 - 32\right)$

$= \frac{3}{5} \left(992\right)$

$= \frac{2976}{5}$