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

The integral from-1 to 3/2 of (x^3-3x) is -55/64

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

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

- \frac{55}{64}

Decimal

- 0.859375

Solution steps

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

\int_{- 1}^{\frac{3}{2}} x^{3} d x = \frac{65}{64}

\int_{- 1}^{\frac{3}{2}} 3 x d x = \frac{15}{8}

= \frac{65}{64} - \frac{15}{8}

Simplify

\frac{65}{64} - \frac{15}{8} : - \frac{55}{64}

= - \frac{55}{64}

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What is the integral from-1 to 3/2 of (x^3-3x) ?
The integral from-1 to 3/2 of (x^3-3x) is -55/64