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

The integral from 0 to 7/2 of-2x^2+7x is 343/24

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integral from 0 to 7/2 of-2x^2+7x

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

\frac{343}{24}

Decimal

14.29166 \dots

Solution steps

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

\int_{0}^{\frac{7}{2}} 2 x^{2} d x = \frac{343}{12}

\int_{0}^{\frac{7}{2}} 7 x d x = \frac{343}{8}

= - \frac{343}{12} + \frac{343}{8}

Simplify

- \frac{343}{12} + \frac{343}{8} : \frac{343}{24}

= \frac{343}{24}

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What is the integral from 0 to 7/2 of-2x^2+7x ?
The integral from 0 to 7/2 of-2x^2+7x is 343/24