What is the integral from 3 to 7 of xsqrt(x-3) ?

The integral from 3 to 7 of xsqrt(x-3) is 144/5

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integral from 3 to 7 of xsqrt(x-3)

\int_{3}^{7} x x - 3 d x

\frac{144}{5}

Decimal Notation

28.8

Solution steps

\int_{3}^{7} x x - 3 d x

Apply u-substitution

: \int_{0}^{4} (u + 3) u d u

= \int_{0}^{4} (u + 3) u d u

Expand

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

= \int_{0}^{4} 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_{0}^{4} u^{\frac{3}{2}} d u + \int_{0}^{4} 3 u d u

\int_{0}^{4} u^{\frac{3}{2}} d u = \frac{64}{5}

\int_{0}^{4} 3 u d u = 16

= \frac{64}{5} + 16

Simplify

\frac{64}{5} + 16 : \frac{144}{5}

= \frac{144}{5}

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What is the integral from 3 to 7 of xsqrt(x-3) ?
The integral from 3 to 7 of xsqrt(x-3) is 144/5