What is the integral from 0 to 4 of (3x-(x^3)/4) ?

The integral from 0 to 4 of (3x-(x^3)/4) is 8

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integral from 0 to 4 of (3x-(x^3)/4)

\int_{0}^{4} (3 x - \frac{x ^{3}}{4}) d x

8

Solution steps

\int_{0}^{4} 3 x - \frac{x ^{3}}{4} 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_{0}^{4} 3 x d x - \int_{0}^{4} \frac{x ^{3}}{4} d x

\int_{0}^{4} 3 x d x = 24

\int_{0}^{4} \frac{x ^{3}}{4} d x = 16

= 24 - 16

Simplify

= 8

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What is the integral from 0 to 4 of (3x-(x^3)/4) ?
The integral from 0 to 4 of (3x-(x^3)/4) is 8