What is the integral from-2 to 4 of (10+4x-3x^3) ?

The integral from-2 to 4 of (10+4x-3x^3) is -96

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integral from-2 to 4 of (10+4x-3x^3)

\int_{- 2}^{4} (10 + 4 x - 3 x^{3}) d x

- 96

Solution steps

\int_{- 2}^{4} 10 + 4 x - 3 x^{3} 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_{- 2}^{4} 10 d x + \int_{- 2}^{4} 4 x d x - \int_{- 2}^{4} 3 x^{3} d x

\int_{- 2}^{4} 10 d x = 60

\int_{- 2}^{4} 4 x d x = 24

\int_{- 2}^{4} 3 x^{3} d x = 180

= 60 + 24 - 180

Simplify

= - 96

What is the integral from-2 to 4 of (10+4x-3x^3) ?
The integral from-2 to 4 of (10+4x-3x^3) is -96