What is the integral from 0 to 4 of |sqrt(x)-1| ?

The integral from 0 to 4 of |sqrt(x)-1| is 2

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integral from 0 to 4 of |sqrt(x)-1|

\int_{0}^{4} x - 1 d x

2

Solution steps

\int_{0}^{4} x - 1 d x

Eliminate Absolutes

= \int_{0}^{1} - x + 1 d x + \int_{1}^{4} x - 1 d x

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

\int_{1}^{4} x - 1 d x = \frac{5}{3}

= \frac{1}{3} + \frac{5}{3}

Simplify

\frac{1}{3} + \frac{5}{3} : 2

= 2

\int_{1}^{4} x^{\frac{1}{2}} d x

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\int_{0}^{\frac{π}{2}} \frac{1}{2 cos ( x ) + 3} d x

What is the integral from 0 to 4 of |sqrt(x)-1| ?
The integral from 0 to 4 of |sqrt(x)-1| is 2