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

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

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integral from 0 to 2 of 1/(sqrt(|x-1|))

\int_{0}^{2} \frac{1}{∣ x - 1 ∣} d x

4

Solution steps

\int_{0}^{2} \frac{1}{∣ x - 1 ∣} d x

Eliminate Absolutes

= \int_{0}^{1} \frac{1}{- x + 1} d x + \int_{1}^{2} \frac{1}{x - 1} d x

\int_{0}^{1} \frac{1}{- x + 1} d x = 2

\int_{1}^{2} \frac{1}{x - 1} d x = 2

= 2 + 2

Simplify

= 4

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