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

The integral from-2 to 3 of (x+2)(x-3) is -125/6

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

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

- \frac{125}{6}

Decimal

- 20.83333 \dots

Solution steps

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

Expand

(x + 2) (x - 3) : x^{2} - x - 6

= \int_{- 2}^{3} x^{2} - x - 6 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} x d x - \int_{- 2}^{3} 6 d x

\int_{- 2}^{3} x^{2} d x = \frac{35}{3}

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

\int_{- 2}^{3} 6 d x = 30

= \frac{35}{3} - \frac{5}{2} - 30

Simplify

\frac{35}{3} - \frac{5}{2} - 30 : - \frac{125}{6}

= - \frac{125}{6}

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What is the integral from-2 to 3 of (x+2)(x-3) ?
The integral from-2 to 3 of (x+2)(x-3) is -125/6