What is the integral from 4 to 9 of xsqrt(x-3) ?

The integral from 4 to 9 of xsqrt(x-3) is (72sqrt(6)-2)/5+12sqrt(6)-2

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integral from 4 to 9 of xsqrt(x-3)

\int_{4}^{9} x x - 3 d x

\frac{72 6 - 2}{5} + 126 - 2

Decimal

62.26652 \dots

Solution steps

\int_{4}^{9} x x - 3 d x

Apply u-substitution

: \int_{1}^{6} (u + 3) u d u

= \int_{1}^{6} (u + 3) u d u

Expand

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

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

\int_{1}^{6} u^{\frac{3}{2}} d u = \frac{72 6 - 2}{5}

\int_{1}^{6} 3 u d u = 126 - 2

= \frac{72 6 - 2}{5} + 126 - 2

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What is the integral from 4 to 9 of xsqrt(x-3) ?
The integral from 4 to 9 of xsqrt(x-3) is (72sqrt(6)-2)/5+12sqrt(6)-2