What is the integral from 0 to 7 of 9x-x^2-2x ?

The integral from 0 to 7 of 9x-x^2-2x is 343/6

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integral from 0 to 7 of 9x-x^2-2x

\int_{0}^{7} 9 x - x^{2} - 2 x d x

\frac{343}{6}

Decimal

57.16666 \dots

Solution steps

\int_{0}^{7} 9 x - x^{2} - 2 x d x

Simplify

= \int_{0}^{7} - x^{2} + 7 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}^{7} x^{2} d x + \int_{0}^{7} 7 x d x

\int_{0}^{7} x^{2} d x = \frac{343}{3}

\int_{0}^{7} 7 x d x = \frac{343}{2}

= - \frac{343}{3} + \frac{343}{2}

Simplify

- \frac{343}{3} + \frac{343}{2} : \frac{343}{6}

= \frac{343}{6}

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What is the integral from 0 to 7 of 9x-x^2-2x ?
The integral from 0 to 7 of 9x-x^2-2x is 343/6