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

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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