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

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

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

\frac{π}{2}

Decimal Notation

1.57079 \dots

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}

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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