What is the integral from 2 to 3 of (x^2+x-12) ?

The integral from 2 to 3 of (x^2+x-12) is -19/6

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integral from 2 to 3 of (x^2+x-12)

\int_{2}^{3} (x^{2} + x - 12) d x

- \frac{19}{6}

Decimal

- 3.16666 \dots

Solution steps

\int_{2}^{3} x^{2} + x - 12 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} 12 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

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

\int_{2}^{3} 12 d x = 12

= \frac{19}{3} + \frac{5}{2} - 12

Simplify

\frac{19}{3} + \frac{5}{2} - 12 : - \frac{19}{6}

= - \frac{19}{6}

What is the integral from 2 to 3 of (x^2+x-12) ?
The integral from 2 to 3 of (x^2+x-12) is -19/6