What is the integral from 0 to 5 of-2x^2+10x ?

The integral from 0 to 5 of-2x^2+10x is 125/3

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integral from 0 to 5 of-2x^2+10x

\int_{0}^{5} - 2 x^{2} + 10 x d x

\frac{125}{3}

Decimal

41.66666 \dots

Solution steps

\int_{0}^{5} - 2 x^{2} + 10 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}^{5} 2 x^{2} d x + \int_{0}^{5} 10 x d x

\int_{0}^{5} 2 x^{2} d x = \frac{250}{3}

\int_{0}^{5} 10 x d x = 125

= - \frac{250}{3} + 125

Simplify

- \frac{250}{3} + 125 : \frac{125}{3}

= \frac{125}{3}

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What is the integral from 0 to 5 of-2x^2+10x ?
The integral from 0 to 5 of-2x^2+10x is 125/3