What is the integral from 0 to 1 of 4/(sqrt(1-x^2)) ?

The integral from 0 to 1 of 4/(sqrt(1-x^2)) is 2pi

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integral from 0 to 1 of 4/(sqrt(1-x^2))

\int_{0}^{1} \frac{4}{1 - x ^{2}} d x

2 π

Decimal Notation

6.28318 \dots

Solution steps

\int_{0}^{1} \frac{4}{1 - x ^{2}} d x

Take the constant out:

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

= 4 \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)

= 4 [arcsin (x)]_{0}^{1}

Compute the boundaries:

\frac{π}{2}

= 4 \cdot \frac{π}{2}

Simplify

= 2 π

x \to 0 lim (\frac{x}{x ^{2} - 9 x})

\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + e ^{- x}})

x^{2} y^{^{'}} + 2 x y = ln (x), y (1) = 3

x, 7, \frac{x ^{2}}{28}

\int - 2 x cos (4 x) d x

What is the integral from 0 to 1 of 4/(sqrt(1-x^2)) ?
The integral from 0 to 1 of 4/(sqrt(1-x^2)) is 2pi