What is the integral from-5 to 3 of (-x^2-2x+15) ?

The integral from-5 to 3 of (-x^2-2x+15) is 256/3

integral from-5 to 3 of (-x^2-2x+15)

\int_{- 5}^{3} (- x^{2} - 2 x + 15) d x

\frac{256}{3}

Decimal

85.33333 \dots

Solution steps

\int_{- 5}^{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_{- 5}^{3} x^{2} d x - \int_{- 5}^{3} 2 x d x + \int_{- 5}^{3} 15 d x

\int_{- 5}^{3} x^{2} d x = \frac{152}{3}

\int_{- 5}^{3} 2 x d x = - 16

\int_{- 5}^{3} 15 d x = 120

= - \frac{152}{3} - (- 16) + 120

Simplify

- \frac{152}{3} - (- 16) + 120 : \frac{256}{3}

= \frac{256}{3}

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What is the integral from-5 to 3 of (-x^2-2x+15) ?
The integral from-5 to 3 of (-x^2-2x+15) is 256/3