What is the integral from 0 to 10 of 10x-x^2 ?

The integral from 0 to 10 of 10x-x^2 is 500/3

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integral from 0 to 10 of 10x-x^2

\int_{0}^{10} 10 x - x^{2} d x

\frac{500}{3}

Decimal

166.66666 \dots

Solution steps

\int_{0}^{10} 10 x - x^{2} 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}^{10} 10 x d x - \int_{0}^{10} x^{2} d x

\int_{0}^{10} 10 x d x = 500

\int_{0}^{10} x^{2} d x = \frac{1000}{3}

= 500 - \frac{1000}{3}

Simplify

500 - \frac{1000}{3} : \frac{500}{3}

= \frac{500}{3}

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What is the integral from 0 to 10 of 10x-x^2 ?
The integral from 0 to 10 of 10x-x^2 is 500/3