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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

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

Use the common integral:

\int \frac{1}{x ^{2} + 1} d x = arctan (x)

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

Compute the boundaries:

\frac{π}{4}

= \frac{π}{4}

\int \frac{2}{2 - x ^{2}} d x

\int \frac{sin ( x )}{cos ^{4} ( x )} d x

\frac{5 x}{( 1 + x ^{2} )}

2 x^{3} + 3 x^{2} - 12 x + 4

\frac{\partial}{\partial x} (x^{2} \cdot y + \frac{x e ^{x}}{y ^{3}})

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