What is the integral from 2 to 3 of (x^2-2x-15) ?

The integral from 2 to 3 of (x^2-2x-15) is -41/3

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integral from 2 to 3 of (x^2-2x-15)

\int_{2}^{3} (x^{2} - 2 x - 15) d x

- \frac{41}{3}

Decimal

- 13.66666 \dots

Solution steps

\int_{2}^{3} 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_{2}^{3} x^{2} d x - \int_{2}^{3} 2 x d x - \int_{2}^{3} 15 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 2 x d x = 5

\int_{2}^{3} 15 d x = 15

= \frac{19}{3} - 5 - 15

Simplify

\frac{19}{3} - 5 - 15 : - \frac{41}{3}

= - \frac{41}{3}

What is the integral from 2 to 3 of (x^2-2x-15) ?
The integral from 2 to 3 of (x^2-2x-15) is -41/3