What is the integral from 5 to 6 of xsqrt(x-5) ?

The integral from 5 to 6 of xsqrt(x-5) is 56/15

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integral from 5 to 6 of xsqrt(x-5)

\int_{5}^{6} x x - 5 d x

\frac{56}{15}

Decimal Notation

3.73333 \dots

Solution steps

\int_{5}^{6} x x - 5 d x

Apply u-substitution

: \int_{0}^{1} (u + 5) u d u

= \int_{0}^{1} (u + 5) u d u

Expand

(u + 5) u : u^{\frac{3}{2}} + 5 u

= \int_{0}^{1} u^{\frac{3}{2}} + 5 u 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_{0}^{1} u^{\frac{3}{2}} d u + \int_{0}^{1} 5 u d u

\int_{0}^{1} u^{\frac{3}{2}} d u = \frac{2}{5}

\int_{0}^{1} 5 u d u = \frac{10}{3}

= \frac{2}{5} + \frac{10}{3}

Simplify

\frac{2}{5} + \frac{10}{3} : \frac{56}{15}

= \frac{56}{15}

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What is the integral from 5 to 6 of xsqrt(x-5) ?
The integral from 5 to 6 of xsqrt(x-5) is 56/15