What is the integral from 2 to 6 of (-x^2+8x-12) ?

The integral from 2 to 6 of (-x^2+8x-12) is 32/3

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integral from 2 to 6 of (-x^2+8x-12)

\int_{2}^{6} (- x^{2} + 8 x - 12) d x

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

\int_{2}^{6} - 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}^{6} x^{2} d x + \int_{2}^{6} 8 x d x - \int_{2}^{6} 12 d x

\int_{2}^{6} x^{2} d x = \frac{208}{3}

\int_{2}^{6} 8 x d x = 128

\int_{2}^{6} 12 d x = 48

= - \frac{208}{3} + 128 - 48

Simplify

- \frac{208}{3} + 128 - 48 : \frac{32}{3}

= \frac{32}{3}

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What is the integral from 2 to 6 of (-x^2+8x-12) ?
The integral from 2 to 6 of (-x^2+8x-12) is 32/3