What is the integral from 0 to 3 of (3x^2-x^3) ?

The integral from 0 to 3 of (3x^2-x^3) is 27/4

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integral from 0 to 3 of (3x^2-x^3)

\int_{0}^{3} (3 x^{2} - x^{3}) d x

\frac{27}{4}

Decimal

6.75

Solution steps

\int_{0}^{3} 3 x^{2} - 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_{0}^{3} 3 x^{2} d x - \int_{0}^{3} x^{3} d x

\int_{0}^{3} 3 x^{2} d x = 27

\int_{0}^{3} x^{3} d x = \frac{81}{4}

= 27 - \frac{81}{4}

Simplify

27 - \frac{81}{4} : \frac{27}{4}

= \frac{27}{4}

\int_{0}^{4} 8 x + x d x

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What is the integral from 0 to 3 of (3x^2-x^3) ?
The integral from 0 to 3 of (3x^2-x^3) is 27/4