What is the integral from 5 to 7 of x^2-2x-15 ?

The integral from 5 to 7 of x^2-2x-15 is 56/3

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integral from 5 to 7 of x^2-2x-15

\int_{5}^{7} x^{2} - 2 x - 15 d x

\frac{56}{3}

Decimal

18.66666 \dots

Solution steps

\int_{5}^{7} 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_{5}^{7} x^{2} d x - \int_{5}^{7} 2 x d x - \int_{5}^{7} 15 d x

\int_{5}^{7} x^{2} d x = \frac{218}{3}

\int_{5}^{7} 2 x d x = 24

\int_{5}^{7} 15 d x = 30

= \frac{218}{3} - 24 - 30

Simplify

\frac{218}{3} - 24 - 30 : \frac{56}{3}

= \frac{56}{3}

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What is the integral from 5 to 7 of x^2-2x-15 ?
The integral from 5 to 7 of x^2-2x-15 is 56/3