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

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

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

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

π

Decimal

3.14159 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

π

= π

\int \frac{4 x - 13}{2 x ^{2} + x - 6} d x

(y - x 4) d x + (x + y 4) d y = 0

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

x^{2} - 1

\frac{d y}{d x} = 4 x e^{2 x}

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