# How do you use limits to find the area between the curve y=2x^3 and the x axis from [1,5]?

Feb 19, 2018

${\int}_{1}^{5} \left(2 {x}^{3}\right) \mathrm{dx} = 312$

#### Explanation:

Given:
$y = 2 {x}^{3}$
lower limit x=1
upper limit x=5
Area bounded by the curve $y = 2 {x}^{3}$, x axis, lower limit x=1, and
upper limit x=5, is given by
${\int}_{1}^{5} y \mathrm{dx}$

$= {\int}_{1}^{5} \left(2 {x}^{3}\right) \mathrm{dx}$

$= \frac{2}{4} \left({x}^{4}\right) {|}_{1}^{5}$

$= \frac{1}{2} \left({5}^{4} - {1}^{4}\right)$

$= \frac{1}{2} \times \left(625 - 1\right)$

$= \frac{1}{2} \times 624$

${\int}_{1}^{5} \left(2 {x}^{3}\right) \mathrm{dx} = 312$