What is the integral from 2 to 5 of (x^2-8x+12) ?

The integral from 2 to 5 of (x^2-8x+12) is -9

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integral from 2 to 5 of (x^2-8x+12)

\int_{2}^{5} (x^{2} - 8 x + 12) d x

- 9

Solution steps

\int_{2}^{5} x^{2} - 8 x + 12 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{2}^{5} x^{2} d x - \int_{2}^{5} 8 x d x + \int_{2}^{5} 12 d x

\int_{2}^{5} x^{2} d x = 39

\int_{2}^{5} 8 x d x = 84

\int_{2}^{5} 12 d x = 36

= 39 - 84 + 36

Simplify

= - 9

What is the integral from 2 to 5 of (x^2-8x+12) ?
The integral from 2 to 5 of (x^2-8x+12) is -9