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### Integral of sin(x)/x

```
Date: 8/29/96 at 2:17:18
From: Anonymous
Subject: sin(x)/x

Would you care to comment on the existence of a symbolic (not a
numerical method) solution to the definite integral of sin(x)/x over,
say, 0 to infinity?
```

```
Date: 8/30/96 at 10:30:58
From: Doctor Jerry
Subject: Re: sin(x)/x

The function

Si(x) = integral from 0 to x of (sin(w)/w) dw

is a well known function.  It is called the sine integral.  To
evaluate Si(x) for any real x requires some kind of numerical
procedure.

You may refer to such books as Handbook of Mathematical Functions,
edited by Milton Abramowitz and Irene A. Stegun, where this function
is tabulated.

They give the value pi/2 for the limit of Si(x) as x approaches
infinity.

If you want to read a symbolic solution, see page 42-42 in Titchmarsh'
Theory of Functions.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
College Calculus
High School Calculus

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