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

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

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

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

- \frac{116}{15}

Decimal Notation

- 7.73333 \dots

Solution steps

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

Expand

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

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

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

\int_{1}^{4} x^{\frac{3}{2}} d x = \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-x)sqrt(x) ?
The integral from 1 to 4 of (1-x)sqrt(x) is -116/15