What is the integral from 0 to 6 of sqrt(6x)-(3x-12) ?

The integral from 0 to 6 of sqrt(6x)-(3x-12) is 42

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integral from 0 to 6 of sqrt(6x)-(3x-12)

\int_{0}^{6} 6 x - (3 x - 12) d x

42

Solution steps

\int_{0}^{6} 6 x - (3 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_{0}^{6} 6 x d x - \int_{0}^{6} 3 x - 12 d x

\int_{0}^{6} 6 x d x = 24

\int_{0}^{6} 3 x - 12 d x = - 18

= 24 - (- 18)

Simplify

= 42

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What is the integral from 0 to 6 of sqrt(6x)-(3x-12) ?
The integral from 0 to 6 of sqrt(6x)-(3x-12) is 42