What is the integral from 0 to 2sqrt(3 of)12x-x^3 ?

The integral from 0 to 2sqrt(3 of)12x-x^3 is 36

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integral from 0 to 2sqrt(3 of)12x-x^3

\int_{0}^{23} 12 x - x^{3} d x

36

Solution steps

\int_{0}^{23} 12 x - x^{3} 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}^{23} 12 x d x - \int_{0}^{23} x^{3} d x

\int_{0}^{23} 12 x d x = 72

\int_{0}^{23} x^{3} d x = 36

= 72 - 36

Simplify

= 36

What is the integral from 0 to 2sqrt(3 of)12x-x^3 ?
The integral from 0 to 2sqrt(3 of)12x-x^3 is 36