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How to integrate Sin(x)/(x)?

by TheDestroyer
Tags: integrate, sinx or x
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kasunjbandara
#19
Mar9-11, 05:37 AM
P: 1
open your MATLAB and insert the operation
then differentiate the answer given by MATLAB
then search the solution reverse....
(start from the final step and come to the first step)

sometimes the above method will work...but even I am not sure about it
djsourabh
#20
Mar9-11, 10:22 PM
P: 59
There could be other way as to go for fourier transform keeping f=0 (frequency )in its equation.If h(x)=\hat{f}(x) then  \hat{h}(\xi)= f(-\xi). that is duality of fourier transform.
Mr.Rabbit87
#21
Jul29-11, 11:59 AM
P: 2
well.... i looked through all the replies to this question and felt that no one really answered it. sooooo

i got the integral to sin(x)/(x) to = -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c

done by integration by parts twice.

so integral of udv = uv - integral of vdu

u = lnx
du = 1/x
dv = sinx
v = -cosx

u get -cosx/x + (integral of cosxlnx) ------ do integration by parts again

u = lnx
du = 1/x
dv = cosx
v = sinx

so u get lnxsinx - (integral of sinx/x). add the (integral of sinx/x) over. So now you have 2(integral of sinx/x) = -cosx/x + lnxsinx

divide the 2 over n you get -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c
Mr.Rabbit87
#22
Jul29-11, 12:03 PM
P: 2
Quote Quote by Mr.Rabbit87 View Post
well.... i looked through all the replies to this question and felt that no one really answered it. sooooo

i got the integral to sin(x)/(x) to = -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c

done by integration by parts twice.

so integral of udv = uv - integral of vdu

u = lnx
du = 1/x
dv = sinx
v = -cosx

u get -cosx/x + (integral of cosxlnx) ------ do integration by parts again

u = lnx
du = 1/x
dv = cosx
v = sinx

so u get lnxsinx - (integral of sinx/x). add the (integral of sinx/x) over. So now you have 2(integral of sinx/x) = -cosx/x + lnxsinx

divide the 2 over n you get -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c
i lied... i differentiate wrong lol
psubpser
#23
May30-13, 01:46 PM
P: 1
Essentially you cannot integrate sin(x)/x in general -- you just get something related to the exponential integral which is defined as the integral of e^x/x.

However, the integral can be done from -infinity to infinity using coutour integrals in the complex plane. See

http://raghumahajan.wordpress.com/20...gral-of-sinxx/


In this case the value of int^infty_infty sin(x)/x is pi.
SteamKing
#24
May31-13, 07:57 PM
Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 6,557
You are trying to find what is called the Sine Integral:

http://en.wikipedia.org/wiki/Trigonometric_integral

Sine integrals and related functions cannot be represented by elementary functions (they are similar to elliptic integrals in this regard).

The value of such functions can be calculated using certain polynomial representations. For example, see Abramowitz and Stegun.


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