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

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

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

\int_{- 1}^{1} \frac{1}{1 - ∣ x ∣} d x

4

Solution steps

\int_{- 1}^{1} \frac{1}{1 - ∣ x ∣} d x

Eliminate Absolutes

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

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

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

= 2 + 2

Simplify

= 4

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