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 -136

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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

- 136

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 = 20

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

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

= 20 + 24 - 180

Simplify

= - 136

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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 -136