What is the integral from 2 to 4 of (x^2-6x+8) ?

The integral from 2 to 4 of (x^2-6x+8) is -4/3

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integral from 2 to 4 of (x^2-6x+8)

\int_{2}^{4} (x^{2} - 6 x + 8) d x

- \frac{4}{3}

Decimal

- 1.33333 \dots

Solution steps

\int_{2}^{4} x^{2} - 6 x + 8 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}^{4} x^{2} d x - \int_{2}^{4} 6 x d x + \int_{2}^{4} 8 d x

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 6 x d x = 36

\int_{2}^{4} 8 d x = 16

= \frac{56}{3} - 36 + 16

Simplify

\frac{56}{3} - 36 + 16 : - \frac{4}{3}

= - \frac{4}{3}

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What is the integral from 2 to 4 of (x^2-6x+8) ?
The integral from 2 to 4 of (x^2-6x+8) is -4/3