What is the integral from-3 to 1 of (x^3+x-5) ?

The integral from-3 to 1 of (x^3+x-5) is -44

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integral from-3 to 1 of (x^3+x-5)

\int_{- 3}^{1} (x^{3} + x - 5) d x

- 44

Solution steps

\int_{- 3}^{1} x^{3} + x - 5 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_{- 3}^{1} x^{3} d x + \int_{- 3}^{1} x d x - \int_{- 3}^{1} 5 d x

\int_{- 3}^{1} x^{3} d x = - 20

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

\int_{- 3}^{1} 5 d x = 20

= - 20 - 4 - 20

Simplify

= - 44

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What is the integral from-3 to 1 of (x^3+x-5) ?
The integral from-3 to 1 of (x^3+x-5) is -44