What is the integral from-4 to-3 of (x^2-2x-15) ?

The integral from-4 to-3 of (x^2-2x-15) is 13/3

integral from-4 to-3 of (x^2-2x-15)

\int_{- 4}^{- 3} (x^{2} - 2 x - 15) d x

\frac{13}{3}

Decimal

4.33333 \dots

Solution steps

\int_{- 4}^{- 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_{- 4}^{- 3} x^{2} d x - \int_{- 4}^{- 3} 2 x d x - \int_{- 4}^{- 3} 15 d x

\int_{- 4}^{- 3} x^{2} d x = \frac{37}{3}

\int_{- 4}^{- 3} 2 x d x = - 7

\int_{- 4}^{- 3} 15 d x = 15

= \frac{37}{3} - (- 7) - 15

Simplify

\frac{37}{3} - (- 7) - 15 : \frac{13}{3}

= \frac{13}{3}

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What is the integral from-4 to-3 of (x^2-2x-15) ?
The integral from-4 to-3 of (x^2-2x-15) is 13/3