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Popular Calculus >

integral from 0 to 5 of x(5-x)

Solution

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

Solution

\frac{125}{6}

+1

Decimal

20.83333 \dots

Solution steps

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

Expand

x (5 - x) : 5 x - x^{2}

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

\int_{0}^{5} 5 x d x = \frac{125}{2}

\int_{0}^{5} x^{2} d x = \frac{125}{3}

= \frac{125}{2} - \frac{125}{3}

Simplify

\frac{125}{2} - \frac{125}{3} : \frac{125}{6}

= \frac{125}{6}

Graph

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 5 of x(5-x) ?
The integral from 0 to 5 of x(5-x) is 125/6