What is the integral from-3/2 to 1/2 of (x^3-4x) ?

The integral from-3/2 to 1/2 of (x^3-4x) is 11/4

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integral from-3/2 to 1/2 of (x^3-4x)

\int_{- \frac{3}{2}}^{\frac{1}{2}} (x^{3} - 4 x) d x

\frac{11}{4}

Decimal

2.75

Solution steps

\int_{- \frac{3}{2}}^{\frac{1}{2}} x^{3} - 4 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_{- \frac{3}{2}}^{\frac{1}{2}} x^{3} d x - \int_{- \frac{3}{2}}^{\frac{1}{2}} 4 x d x

\int_{- \frac{3}{2}}^{\frac{1}{2}} x^{3} d x = - \frac{5}{4}

\int_{- \frac{3}{2}}^{\frac{1}{2}} 4 x d x = - 4

= - \frac{5}{4} - (- 4)

Simplify

- \frac{5}{4} - (- 4) : \frac{11}{4}

= \frac{11}{4}

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What is the integral from-3/2 to 1/2 of (x^3-4x) ?
The integral from-3/2 to 1/2 of (x^3-4x) is 11/4