What is the integral from-6 to 1 of-x^2-3x ?

The integral from-6 to 1 of-x^2-3x is -119/6

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integral from-6 to 1 of-x^2-3x

\int_{- 6}^{1} - x^{2} - 3 x d x

- \frac{119}{6}

Solution steps

\int_{- 6}^{1} - x^{2} - 3 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_{- 6}^{1} x^{2} d x - \int_{- 6}^{1} 3 x d x

\int_{- 6}^{1} x^{2} d x = \frac{217}{3}

\int_{- 6}^{1} 3 x d x = - \frac{105}{2}

= - \frac{217}{3} - (- \frac{105}{2})

Simplify

- \frac{217}{3} - (- \frac{105}{2}) : - \frac{119}{6}

= - \frac{119}{6}

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What is the integral from-6 to 1 of-x^2-3x ?
The integral from-6 to 1 of-x^2-3x is -119/6