What is the integral from 2 to 3 of-x^2+5x-6 ?

The integral from 2 to 3 of-x^2+5x-6 is 1/6

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integral from 2 to 3 of-x^2+5x-6

\int_{2}^{3} - x^{2} + 5 x - 6 d x

\frac{1}{6}

Decimal

0.16666 \dots

Solution steps

\int_{2}^{3} - x^{2} + 5 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} 5 x d x - \int_{2}^{3} 6 d x

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

\int_{2}^{3} 5 x d x = \frac{25}{2}

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

= - \frac{19}{3} + \frac{25}{2} - 6

Simplify

- \frac{19}{3} + \frac{25}{2} - 6 : \frac{1}{6}

= \frac{1}{6}

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What is the integral from 2 to 3 of-x^2+5x-6 ?
The integral from 2 to 3 of-x^2+5x-6 is 1/6