What is the integral from 0 to 1 of (u+7)(u-8) ?

The integral from 0 to 1 of (u+7)(u-8) is -337/6

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integral from 0 to 1 of (u+7)(u-8)

\int_{0}^{1} (u + 7) (u - 8) d u

- \frac{337}{6}

Solution steps

\int_{0}^{1} (u + 7) (u - 8) d u

Expand

(u + 7) (u - 8) : u^{2} - u - 56

= \int_{0}^{1} u^{2} - u - 56 d u

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}^{1} u^{2} d u - \int_{0}^{1} u d u - \int_{0}^{1} 56 d u

\int_{0}^{1} u^{2} d u = \frac{1}{3}

\int_{0}^{1} u d u = \frac{1}{2}

\int_{0}^{1} 56 d u = 56

= \frac{1}{3} - \frac{1}{2} - 56

Simplify

\frac{1}{3} - \frac{1}{2} - 56 : - \frac{337}{6}

= - \frac{337}{6}

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What is the integral from 0 to 1 of (u+7)(u-8) ?
The integral from 0 to 1 of (u+7)(u-8) is -337/6