What is the integral from 0 to 4 of (5-x)sqrt(x) ?

The integral from 0 to 4 of (5-x)sqrt(x) is 208/15

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integral from 0 to 4 of (5-x)sqrt(x)

\int_{0}^{4} (5 - x) x d x

\frac{208}{15}

Decimal

13.86666 \dots

Solution steps

\int_{0}^{4} (5 - x) x d x

Expand

(5 - x) x : 5 x - x^{\frac{3}{2}}

= \int_{0}^{4} 5 x - x^{\frac{3}{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}^{4} 5 x d x - \int_{0}^{4} x^{\frac{3}{2}} d x

\int_{0}^{4} 5 x d x = \frac{80}{3}

\int_{0}^{4} x^{\frac{3}{2}} d x = \frac{64}{5}

= \frac{80}{3} - \frac{64}{5}

Simplify

\frac{80}{3} - \frac{64}{5} : \frac{208}{15}

= \frac{208}{15}

What is the integral from 0 to 4 of (5-x)sqrt(x) ?
The integral from 0 to 4 of (5-x)sqrt(x) is 208/15