What is the integral from 0 to 4 of 3x^3-3x+1 ?

The integral from 0 to 4 of 3x^3-3x+1 is 172

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integral from 0 to 4 of 3x^3-3x+1

\int_{0}^{4} 3 x^{3} - 3 x + 1 d x

172

Solution steps

\int_{0}^{4} 3 x^{3} - 3 x + 1 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} 3 x^{3} d x - \int_{0}^{4} 3 x d x + \int_{0}^{4} 1 d x

\int_{0}^{4} 3 x^{3} d x = 192

\int_{0}^{4} 3 x d x = 24

\int_{0}^{4} 1 d x = 4

= 192 - 24 + 4

Simplify

= 172

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What is the integral from 0 to 4 of 3x^3-3x+1 ?
The integral from 0 to 4 of 3x^3-3x+1 is 172