What is the integral from 0 to 5 of (5x^2-x^3) ?

The integral from 0 to 5 of (5x^2-x^3) is 625/12

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integral from 0 to 5 of (5x^2-x^3)

\int_{0}^{5} (5 x^{2} - x^{3}) d x

\frac{625}{12}

Decimal

52.08333 \dots

Solution steps

\int_{0}^{5} 5 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}^{5} 5 x^{2} d x - \int_{0}^{5} x^{3} d x

\int_{0}^{5} 5 x^{2} d x = \frac{625}{3}

\int_{0}^{5} x^{3} d x = \frac{625}{4}

= \frac{625}{3} - \frac{625}{4}

Simplify

\frac{625}{3} - \frac{625}{4} : \frac{625}{12}

= \frac{625}{12}

What is the integral from 0 to 5 of (5x^2-x^3) ?
The integral from 0 to 5 of (5x^2-x^3) is 625/12