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

The integral from 2 to 4 of (3x^2-(x^3)/4) is 41

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

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

41

Solution steps

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

\int_{2}^{4} 3 x^{2} d x = 56

\int_{2}^{4} \frac{x ^{3}}{4} d x = 15

= 56 - 15

Simplify

= 41

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What is the integral from 2 to 4 of (3x^2-(x^3)/4) ?
The integral from 2 to 4 of (3x^2-(x^3)/4) is 41