What is the integral from 0 to 3 of (2x^3-2x-1) ?

The integral from 0 to 3 of (2x^3-2x-1) is 57/2

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integral from 0 to 3 of (2x^3-2x-1)

\int_{0}^{3} (2 x^{3} - 2 x - 1) d x

\frac{57}{2}

Decimal

28.5

Solution steps

\int_{0}^{3} 2 x^{3} - 2 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}^{3} 2 x^{3} d x - \int_{0}^{3} 2 x d x - \int_{0}^{3} 1 d x

\int_{0}^{3} 2 x^{3} d x = \frac{81}{2}

\int_{0}^{3} 2 x d x = 9

\int_{0}^{3} 1 d x = 3

= \frac{81}{2} - 9 - 3

Simplify

\frac{81}{2} - 9 - 3 : \frac{57}{2}

= \frac{57}{2}

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What is the integral from 0 to 3 of (2x^3-2x-1) ?
The integral from 0 to 3 of (2x^3-2x-1) is 57/2