What is the integral from 1 to 12 of-x^2-11x+12 ?

The integral from 1 to 12 of-x^2-11x+12 is -7381/6

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integral from 1 to 12 of-x^2-11x+12

\int_{1}^{12} - x^{2} - 11 x + 12 d x

- \frac{7381}{6}

Decimal Notation

- 1230.16666 \dots

Solution steps

\int_{1}^{12} - x^{2} - 11 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_{1}^{12} x^{2} d x - \int_{1}^{12} 11 x d x + \int_{1}^{12} 12 d x

\int_{1}^{12} x^{2} d x = \frac{1727}{3}

\int_{1}^{12} 11 x d x = \frac{1573}{2}

\int_{1}^{12} 12 d x = 132

= - \frac{1727}{3} - \frac{1573}{2} + 132

Simplify

- \frac{1727}{3} - \frac{1573}{2} + 132 : - \frac{7381}{6}

= - \frac{7381}{6}

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What is the integral from 1 to 12 of-x^2-11x+12 ?
The integral from 1 to 12 of-x^2-11x+12 is -7381/6