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

The integral from 0 to infinity of 2/(1+t^2) is pi

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

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t

π

Decimal

3.14159 \dots

Solution steps

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t = π - 0

= π - 0

Simplify

= π

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