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

The integral from-1 to 3 of (-x^3+2x-11) is -56

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integral from-1 to 3 of (-x^3+2x-11)

\int_{- 1}^{3} (- x^{3} + 2 x - 11) d x

- 56

Solution steps

\int_{- 1}^{3} - x^{3} + 2 x - 11 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}^{3} x^{3} d x + \int_{- 1}^{3} 2 x d x - \int_{- 1}^{3} 11 d x

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

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

\int_{- 1}^{3} 11 d x = 44

= - 20 + 8 - 44

Simplify

= - 56

t^{3} e^{t}

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What is the integral from-1 to 3 of (-x^3+2x-11) ?
The integral from-1 to 3 of (-x^3+2x-11) is -56