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

The integral from 0 to 3 of (1/2 x^3-3x) is -27/8

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

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

- \frac{27}{8}

Decimal

- 3.375

Solution steps

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

\int_{0}^{3} \frac{1}{2} x^{3} d x = \frac{81}{8}

\int_{0}^{3} 3 x d x = \frac{27}{2}

= \frac{81}{8} - \frac{27}{2}

Simplify

\frac{81}{8} - \frac{27}{2} : - \frac{27}{8}

= - \frac{27}{8}

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What is the integral from 0 to 3 of (1/2 x^3-3x) ?
The integral from 0 to 3 of (1/2 x^3-3x) is -27/8