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

The integral from 0 to 1 of 1/(sqrt(1-x^2)) is pi/2

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

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

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{1 - x ^{2}} d x = arcsin (x)

= [arcsin (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2}

= \frac{π}{2}

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