# How do you find the integral of x^2-6x+5 from the interval [0,3]?

May 13, 2018

-3

#### Explanation:

We can use the reverse power rule:

$f \left(x\right) = {x}^{2} - 6 x + 5 {x}^{0}$

Therefore,

${\int}_{0}^{3} {x}^{2} - 6 x + 5 {x}^{0} \mathrm{dx} = {\left[{x}^{3} / 3 - 6 {x}^{2} / 2 + 5 {x}^{1} / 1\right]}_{0}^{3}$

This is equivalent to:

(27/3-3(9)+5(3)-(0/3-6*0/2+5(0))

Therefore, the answer is -3. Note that the definite integral gives the net area under the graph. The negative sign implies that there is more area below the x-axis (than above) for the interval from 0 to 3 (inclusive).

If you are unfamiliar with the reverse power rule, this might help: https://www.khanacademy.org/math/ap-calculus-ab/ab-antiderivatives-ftc/ab-reverse-power-rule/v/indefinite-integrals-of-x-raised-to-a-power