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

The integral from-5 to 0 of (x^2+5x) is -125/6

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

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

- \frac{125}{6}

Decimal

- 20.83333 \dots

Solution steps

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

\int_{- 5}^{0} x^{2} d x = \frac{125}{3}

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

= \frac{125}{3} - \frac{125}{2}

Simplify

\frac{125}{3} - \frac{125}{2} : - \frac{125}{6}

= - \frac{125}{6}

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What is the integral from-5 to 0 of (x^2+5x) ?
The integral from-5 to 0 of (x^2+5x) is -125/6