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

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

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

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

arcsin (y)

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

arcsin (y)

= arcsin (y)

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