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

The integral from 0 to 5/2 of 5x-2x^2 is 125/24

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integral from 0 to 5/2 of 5x-2x^2

\int_{0}^{\frac{5}{2}} 5 x - 2 x^{2} d x

\frac{125}{24}

Decimal

5.20833 \dots

Solution steps

\int_{0}^{\frac{5}{2}} 5 x - 2 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}^{\frac{5}{2}} 5 x d x - \int_{0}^{\frac{5}{2}} 2 x^{2} d x

\int_{0}^{\frac{5}{2}} 5 x d x = \frac{125}{8}

\int_{0}^{\frac{5}{2}} 2 x^{2} d x = \frac{125}{12}

= \frac{125}{8} - \frac{125}{12}

Simplify

\frac{125}{8} - \frac{125}{12} : \frac{125}{24}

= \frac{125}{24}

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What is the integral from 0 to 5/2 of 5x-2x^2 ?
The integral from 0 to 5/2 of 5x-2x^2 is 125/24