What is the integral from 2 to 3 of (x^2-8x+12) ?

The integral from 2 to 3 of (x^2-8x+12) is -5/3

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integral from 2 to 3 of (x^2-8x+12)

\int_{2}^{3} (x^{2} - 8 x + 12) d x

- \frac{5}{3}

Decimal Notation

- 1.66666 \dots

Solution steps

\int_{2}^{3} 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}^{3} x^{2} d x - \int_{2}^{3} 8 x d x + \int_{2}^{3} 12 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 8 x d x = 20

\int_{2}^{3} 12 d x = 12

= \frac{19}{3} - 20 + 12

Simplify

\frac{19}{3} - 20 + 12 : - \frac{5}{3}

= - \frac{5}{3}

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What is the integral from 2 to 3 of (x^2-8x+12) ?
The integral from 2 to 3 of (x^2-8x+12) is -5/3