What is the integral from 0 to 4 of-6x^2-24x+192 ?

The integral from 0 to 4 of-6x^2-24x+192 is 448

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integral from 0 to 4 of-6x^2-24x+192

\int_{0}^{4} - 6 x^{2} - 24 x + 192 d x

448

Solution steps

\int_{0}^{4} - 6 x^{2} - 24 x + 192 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}^{4} 6 x^{2} d x - \int_{0}^{4} 24 x d x + \int_{0}^{4} 192 d x

\int_{0}^{4} 6 x^{2} d x = 128

\int_{0}^{4} 24 x d x = 192

\int_{0}^{4} 192 d x = 768

= - 128 - 192 + 768

Simplify

= 448

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What is the integral from 0 to 4 of-6x^2-24x+192 ?
The integral from 0 to 4 of-6x^2-24x+192 is 448