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

The integral from-1 to 3 of (-x)^3 is -20

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

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

- 20

Solution steps

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

Simplify

(- x)^{3} : - x^{3}

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: [\frac{x ^{4}}{4}]_{- 1}^{3}

= - [\frac{x ^{4}}{4}]_{- 1}^{3}

Compute the boundaries:

20

= - 20

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What is the integral from-1 to 3 of (-x)^3 ?
The integral from-1 to 3 of (-x)^3 is -20