Question

What is the net area between `f(x)=x^3-x^2+5` in `x in[2,5]` and the x-axis?

Answer 1

128.25

Explanation:

the area under a curve from point a to point b is the Definite integral of that curve evaluated from point a to point b

therefore,
area from a to b under the curve `f(x) = int_a^b f(x) dx`

therefore, after integrating your above function
we get its antiderivative as
`F(x) = 1/4x^3 - 1/3x^2 + 5x`

the antiderivative of `f(x)` Is usually named as `F(x)`

now, Subtract the value of `F(x)` at `a` from its value at `b`

`= F(b) - F(a)`

and you get
`128.25`
=