What is the integral from 7 to 10 of xsqrt(x-6) ?

The integral from 7 to 10 of xsqrt(x-6) is 202/5

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integral from 7 to 10 of xsqrt(x-6)

\int_{7}^{10} x x - 6 d x

\frac{202}{5}

Decimal

40.4

Solution steps

\int_{7}^{10} x x - 6 d x

Apply u-substitution

= \int_{1}^{4} (u + 6) u d u

Expand

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

= \int_{1}^{4} 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_{1}^{4} u^{\frac{3}{2}} d u + \int_{1}^{4} 6 u d u

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

\int_{1}^{4} 6 u d u = 28

= \frac{62}{5} + 28

Simplify

\frac{62}{5} + 28 : \frac{202}{5}

= \frac{202}{5}

What is the integral from 7 to 10 of xsqrt(x-6) ?
The integral from 7 to 10 of xsqrt(x-6) is 202/5