What is the integral from 0 to 9 of |sqrt(x)-1| ?

The integral from 0 to 9 of |sqrt(x)-1| is 29/3

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integral from 0 to 9 of |sqrt(x)-1|

\int_{0}^{9} x - 1 d x

\frac{29}{3}

Decimal

9.66666 \dots

Solution steps

\int_{0}^{9} x - 1 d x

Eliminate Absolutes

= \int_{0}^{1} - x + 1 d x + \int_{1}^{9} x - 1 d x

\int_{0}^{1} - x + 1 d x = \frac{1}{3}

\int_{1}^{9} x - 1 d x = \frac{28}{3}

= \frac{1}{3} + \frac{28}{3}

Simplify

\frac{1}{3} + \frac{28}{3} : \frac{29}{3}

= \frac{29}{3}

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What is the integral from 0 to 9 of |sqrt(x)-1| ?
The integral from 0 to 9 of |sqrt(x)-1| is 29/3