What is the integral from 0 to 6 of-5/12 x^2-5x ?

The integral from 0 to 6 of-5/12 x^2-5x is -120

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integral from 0 to 6 of-5/12 x^2-5x

\int_{0}^{6} - \frac{5}{12} x^{2} - 5 x d x

- 120

Solution steps

\int_{0}^{6} - \frac{5}{12} x^{2} - 5 x 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_{0}^{6} \frac{5}{12} x^{2} d x - \int_{0}^{6} 5 x d x

\int_{0}^{6} \frac{5}{12} x^{2} d x = 30

\int_{0}^{6} 5 x d x = 90

= - 30 - 90

Simplify

= - 120

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What is the integral from 0 to 6 of-5/12 x^2-5x ?
The integral from 0 to 6 of-5/12 x^2-5x is -120