What is the integral from-2 to 0 of (x-3)(x+5) ?

The integral from-2 to 0 of (x-3)(x+5) is -94/3

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integral from-2 to 0 of (x-3)(x+5)

\int_{- 2}^{0} (x - 3) (x + 5) d x

- \frac{94}{3}

Decimal Notation

- 31.33333 \dots

Solution steps

\int_{- 2}^{0} (x - 3) (x + 5) d x

Expand

(x - 3) (x + 5) : x^{2} + 2 x - 15

= \int_{- 2}^{0} 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}^{0} x^{2} d x + \int_{- 2}^{0} 2 x d x - \int_{- 2}^{0} 15 d x

\int_{- 2}^{0} x^{2} d x = \frac{8}{3}

\int_{- 2}^{0} 2 x d x = - 4

\int_{- 2}^{0} 15 d x = 30

= \frac{8}{3} - 4 - 30

Simplify

\frac{8}{3} - 4 - 30 : - \frac{94}{3}

= - \frac{94}{3}

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What is the integral from-2 to 0 of (x-3)(x+5) ?
The integral from-2 to 0 of (x-3)(x+5) is -94/3