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

Mar 4, 2018

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 $f \left(x\right) = {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

therefore, after integrating your above function
we get its antiderivative as
$F \left(x\right) = \frac{1}{4} {x}^{3} - \frac{1}{3} {x}^{2} + 5 x$

the antiderivative of $f \left(x\right)$ Is usually named as $F \left(x\right)$

now, Subtract the value of $F \left(x\right)$ at $a$ from its value at $b$

# $= F \left(b\right) - F \left(a\right)$

and you get
$128.25$
=