Question

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

Answer 1

`int_1^5(2x^3)dx=312`

Explanation:

Given:
`y=2x^3`
lower limit x=1
upper limit x=5
Area bounded by the curve `y=2x^3`, x axis, lower limit x=1, and
upper limit x=5, is given by
`int_1^5ydx`

`=int_1^5(2x^3)dx`

`=2/4(x^4)|_1^5`

`=1/2(5^4-1^4)`

`=1/2xx(625-1)`

`=1/2xx624`

`int_1^5(2x^3)dx=312`