What is the integral from 2 to 6 of 2x^2-16x+24 ?

The integral from 2 to 6 of 2x^2-16x+24 is -64/3

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integral from 2 to 6 of 2x^2-16x+24

\int_{2}^{6} 2 x^{2} - 16 x + 24 d x

- \frac{64}{3}

Decimal

- 21.33333 \dots

Solution steps

\int_{2}^{6} 2 x^{2} - 16 x + 24 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} 2 x^{2} d x - \int_{2}^{6} 16 x d x + \int_{2}^{6} 24 d x

\int_{2}^{6} 2 x^{2} d x = \frac{416}{3}

\int_{2}^{6} 16 x d x = 256

\int_{2}^{6} 24 d x = 96

= \frac{416}{3} - 256 + 96

Simplify

\frac{416}{3} - 256 + 96 : - \frac{64}{3}

= - \frac{64}{3}

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What is the integral from 2 to 6 of 2x^2-16x+24 ?
The integral from 2 to 6 of 2x^2-16x+24 is -64/3