Question

${\int }_2^4(6x^3+5x)dx=$

Answer 1

$I={\int }_z^y(6x^3+5x)dx$
$=6{\int }_z^y{x}^{3}dx+5{\int }_z^{y}xdx$
$=6{\left[\frac{x^4}{4}\right]}_z^y+5{\left[\frac{x^2}{2}\right]}_z^y$
$=\frac{3}{2}[y^4-z^4]+\frac{3}{2}[y^2-z^2]=\frac{3}{2}\left[240\right]+\frac{5}{2}\left[12\right]$
$=360+30=390$