What is the integral from 6 to 7 of (xsqrt(x-6)) ?

The integral from 6 to 7 of (xsqrt(x-6)) is 22/5

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integral from 6 to 7 of (xsqrt(x-6))

\int_{6}^{7} (x x - 6) d x

\frac{22}{5}

Decimal

4.4

Solution steps

\int_{6}^{7} x x - 6 d x

Apply u-substitution

: \int_{0}^{1} (u + 6) u d u

= \int_{0}^{1} (u + 6) u d u

Expand

(u + 6) u : u^{\frac{3}{2}} + 6 u

= \int_{0}^{1} u^{\frac{3}{2}} + 6 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} 6 u d u

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

\int_{0}^{1} 6 u d u = 4

= \frac{2}{5} + 4

Simplify

\frac{2}{5} + 4 : \frac{22}{5}

= \frac{22}{5}

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What is the integral from 6 to 7 of (xsqrt(x-6)) ?
The integral from 6 to 7 of (xsqrt(x-6)) is 22/5