Question

How to find area of the function: f(x)=e^3, g(x)=x^3 , x=0 and x=1?

I don't really understand the "e" part.
Thanks <3

Answer 1

Area `approx 19.835537` sq units
[Assuming you mean the area bounded by:
`f(x)=e^3, g(x)=x^3, x=0 and x=1`]

Explanation:

I assume you mean the area bounded by:
`f(x)=e^3, g(x)=x^3, x=0 and x=1`

First note that `e` is a constant `approx 2.718282`

So `e^3 approx 20.085537`

Then the area bounded by `f(x)=e^3, x=0 and x=1` and the `x-`axis is a rectangle with sides `approx 20.085537 and 1`

Hence this rectangle has an area of `approx 20.085537` sq units.

So, the area bounded by: `f(x)=e^3, g(x)=x^3, x=0 and x=1` will equal:

`approx 20.085537 - int_0^1 x^3 dx`

`approx 20.085537 - x^4/4|_0^1`

`approx 20.085537 - 0.25`

`approx 19.835537` sq units