What is the integral from 0 to 8 of (-x^2+8x) ?

The integral from 0 to 8 of (-x^2+8x) is 256/3

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integral from 0 to 8 of (-x^2+8x)

\int_{0}^{8} (- x^{2} + 8 x) d x

\frac{256}{3}

Decimal

85.33333 \dots

Solution steps

\int_{0}^{8} - x^{2} + 8 x 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_{0}^{8} x^{2} d x + \int_{0}^{8} 8 x d x

\int_{0}^{8} x^{2} d x = \frac{512}{3}

\int_{0}^{8} 8 x d x = 256

= - \frac{512}{3} + 256

Simplify

- \frac{512}{3} + 256 : \frac{256}{3}

= \frac{256}{3}

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What is the integral from 0 to 8 of (-x^2+8x) ?
The integral from 0 to 8 of (-x^2+8x) is 256/3