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

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

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

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

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

\frac{π}{2}

= \frac{π}{2}

\int_{0}^{π} sin (t) cos (t) d t

\int_{0}^{x^{2}} cos (t^{2}) d t

\int_{0}^{1} (e^{x} + 1) d x

\int_{2}^{5} (6 + cos (\frac{x}{10})) d x

\int_{0}^{π} x cos (2 x) d x

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