What is the integral from 4 to 16 of (x-1)sqrt(x) ?

The integral from 4 to 16 of (x-1)sqrt(x) is 5392/15

integral from 4 to 16 of (x-1)sqrt(x)

\int_{4}^{16} (x - 1) x d x

\frac{5392}{15}

Decimal

359.46666 \dots

Solution steps

\int_{4}^{16} (x - 1) x d x

Expand

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

= \int_{4}^{16} x^{\frac{3}{2}} - x 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_{4}^{16} x^{\frac{3}{2}} d x - \int_{4}^{16} x d x

\int_{4}^{16} x^{\frac{3}{2}} d x = \frac{1984}{5}

\int_{4}^{16} x d x = \frac{112}{3}

= \frac{1984}{5} - \frac{112}{3}

Simplify

\frac{1984}{5} - \frac{112}{3} : \frac{5392}{15}

= \frac{5392}{15}

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What is the integral from 4 to 16 of (x-1)sqrt(x) ?
The integral from 4 to 16 of (x-1)sqrt(x) is 5392/15