What is the integral from 1 to 6 of x^2-4x-12 ?

The integral from 1 to 6 of x^2-4x-12 is -175/3

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integral from 1 to 6 of x^2-4x-12

\int_{1}^{6} x^{2} - 4 x - 12 d x

- \frac{175}{3}

Decimal

- 58.33333 \dots

Solution steps

\int_{1}^{6} x^{2} - 4 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}^{6} x^{2} d x - \int_{1}^{6} 4 x d x - \int_{1}^{6} 12 d x

\int_{1}^{6} x^{2} d x = \frac{215}{3}

\int_{1}^{6} 4 x d x = 70

\int_{1}^{6} 12 d x = 60

= \frac{215}{3} - 70 - 60

Simplify

\frac{215}{3} - 70 - 60 : - \frac{175}{3}

= - \frac{175}{3}

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What is the integral from 1 to 6 of x^2-4x-12 ?
The integral from 1 to 6 of x^2-4x-12 is -175/3