What is the integral from 5 to 6 of x^2+x-14 ?

The integral from 5 to 6 of x^2+x-14 is 131/6

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integral from 5 to 6 of x^2+x-14

\int_{5}^{6} x^{2} + x - 14 d x

\frac{131}{6}

Decimal

21.83333 \dots

Solution steps

\int_{5}^{6} x^{2} + x - 14 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}^{6} x^{2} d x + \int_{5}^{6} x d x - \int_{5}^{6} 14 d x

\int_{5}^{6} x^{2} d x = \frac{91}{3}

\int_{5}^{6} x d x = \frac{11}{2}

\int_{5}^{6} 14 d x = 14

= \frac{91}{3} + \frac{11}{2} - 14

Simplify

\frac{91}{3} + \frac{11}{2} - 14 : \frac{131}{6}

= \frac{131}{6}

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What is the integral from 5 to 6 of x^2+x-14 ?
The integral from 5 to 6 of x^2+x-14 is 131/6