What is the integral from 1 to 4 of (1-u)sqrt(u) ?

The integral from 1 to 4 of (1-u)sqrt(u) is -116/15

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integral from 1 to 4 of (1-u)sqrt(u)

\int_{1}^{4} (1 - u) u d u

- \frac{116}{15}

Decimal

- 7.73333 \dots

Solution steps

\int_{1}^{4} (1 - u) u d u

Expand

(1 - u) u : u - u^{\frac{3}{2}}

= \int_{1}^{4} u - u^{\frac{3}{2}} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{4} u d u - \int_{1}^{4} u^{\frac{3}{2}} d u

\int_{1}^{4} u d u = \frac{14}{3}

\int_{1}^{4} u^{\frac{3}{2}} d u = \frac{62}{5}

= \frac{14}{3} - \frac{62}{5}

Simplify

\frac{14}{3} - \frac{62}{5} : - \frac{116}{15}

= - \frac{116}{15}

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What is the integral from 1 to 4 of (1-u)sqrt(u) ?
The integral from 1 to 4 of (1-u)sqrt(u) is -116/15