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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= 2 [arcsin (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2}

= 2 \cdot \frac{π}{2}

Simplify

= π

\frac{\partial}{\partial y} (\frac{x + 1}{y - 1})

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

\int y y + 1 d y

y = 5 x - x^{2}

4 tan^{2} (3 x)

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