What is the integral from-1 to 1 of 1/(1+y^2) ?

The integral from-1 to 1 of 1/(1+y^2) is pi/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 1 of 1/(1+y^2)

\int_{- 1}^{1} \frac{1}{1 + y ^{2}} d y

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{- 1}^{1} \frac{1}{1 + y ^{2}} d y

Use the common integral:

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

= [arctan (y)]_{- 1}^{1}

Compute the boundaries:

\frac{π}{2}

= \frac{π}{2}

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