What is the integral from 0 to infinity of ((sin(x))/x) ?

The integral from 0 to infinity of ((sin(x))/x) is pi/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to infinity of ((sin(x))/x)

\int_{0}^{\infty} (\frac{sin ( x )}{x}) d x

\frac{π}{2}

Solution steps

\int_{0}^{\infty} \frac{sin ( x )}{x} d x

Compute the indefinite integral:

\int \frac{sin ( x )}{x} d x = Si (x) + C

Compute the boundaries:

\int_{0}^{\infty} (\frac{sin ( x )}{x}) d x = \frac{π}{2} - 0

= \frac{π}{2} - 0

Simplify

= \frac{π}{2}

\int_{0}^{x} ln (1 + x) d x

\int_{0}^{0.3} x ln (1 + x^{3}) d x

\int_{1}^{2} (3 x^{3} + \frac{6}{x ^{2}}) d x

\int_{- 2}^{2} x^{5} d x

\int_{2}^{x^{3}} \frac{1}{t ^{3}} d t

What is the integral from 0 to infinity of ((sin(x))/x) ?
The integral from 0 to infinity of ((sin(x))/x) is pi/2