What is the integral from 1 to 6 of (x^2-2x-15) ?

The integral from 1 to 6 of (x^2-2x-15) is -115/3

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integral from 1 to 6 of (x^2-2x-15)

\int_{1}^{6} (x^{2} - 2 x - 15) d x

- \frac{115}{3}

Decimal

- 38.33333 \dots

Solution steps

\int_{1}^{6} x^{2} - 2 x - 15 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_{1}^{6} x^{2} d x - \int_{1}^{6} 2 x d x - \int_{1}^{6} 15 d x

\int_{1}^{6} x^{2} d x = \frac{215}{3}

\int_{1}^{6} 2 x d x = 35

\int_{1}^{6} 15 d x = 75

= \frac{215}{3} - 35 - 75

Simplify

\frac{215}{3} - 35 - 75 : - \frac{115}{3}

= - \frac{115}{3}

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What is the integral from 1 to 6 of (x^2-2x-15) ?
The integral from 1 to 6 of (x^2-2x-15) is -115/3