What is the integral from 0 to 5 of (-3x-5x^2) ?

The integral from 0 to 5 of (-3x-5x^2) is -1475/6

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integral from 0 to 5 of (-3x-5x^2)

\int_{0}^{5} (- 3 x - 5 x^{2}) d x

- \frac{1475}{6}

Decimal Notation

- 245.83333 \dots

Solution steps

\int_{0}^{5} - 3 x - 5 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}^{5} 3 x d x - \int_{0}^{5} 5 x^{2} d x

\int_{0}^{5} 3 x d x = \frac{75}{2}

\int_{0}^{5} 5 x^{2} d x = \frac{625}{3}

= - \frac{75}{2} - \frac{625}{3}

Simplify

- \frac{75}{2} - \frac{625}{3} : - \frac{1475}{6}

= - \frac{1475}{6}

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What is the integral from 0 to 5 of (-3x-5x^2) ?
The integral from 0 to 5 of (-3x-5x^2) is -1475/6