Home » Ask & Discuss » Mathematics. » Integral Calculus « Back to Discussion

Integral Calculus

New kid on the Block

Joined:	28 Feb 2009
Post:	1

2 May 2009 12:56:14 IST

0 People liked this

1419

Integration of sin(x)/x

None

Integration of sin(x)/x

Share this article on:

Comments (7)

geniussam

Hot goIITian

Joined: 30 Nov 2008

Posts: 110

2 May 2009 13:04:09 IST

Like 0 people liked this

apply integration by parts

taran

Blazing goIITian

Joined: 17 Nov 2008

Posts: 1331

2 May 2009 19:09:29 IST

Like 0 people liked this

hello is sinx/x integrable ?

Sujit

Blazing goIITian

Joined: 11 Mar 2009

Posts: 1345

2 May 2009 19:12:10 IST

Like 0 people liked this

its a non integrable function...check any standard books

namita lohani

Hot goIITian

Joined: 14 Jul 2008

Posts: 178

3 May 2009 04:32:31 IST

Like 0 people liked this

IT IS NOT INTEGRABLE.......FOR REFERENCE YOU CAN SEE ARIHANT INTEGRAL CALCULAS ITS GIVEN THERE

Anant Kumar

Forum Expert

Joined: 10 Jul 2008

Posts: 598

4 May 2009 13:01:23 IST

Like 1 people liked this

Of course, it is integrable. Only thing is that we cannot express the integral in terms of the basic elementary functions. So in a sense, the integral of $\dfrac{\sin x}{x}$ is a higher function (or you can say that its a new function). For example, consider
$F(x)=\int_0^x \dfrac{\sin t}{t}\ \mathrm{d}t + C$ (here $C$ is an arbitrary constant)
Then, differentiating w.r.t. the upper limit $x$ , we get
$\dfrac{\mathrm{d}F(x)}{\mathrm{d}x}=\dfrac{\sin x}{x}$
As such, we can take $F(x)$ as the indefinite integral of $\dfrac{\sin x}{x}$

Bhushan Gosavi

New kid on the Block

Joined: 4 May 2009

Posts: 7

4 May 2009 13:04:26 IST

Like 0 people liked this

solve it by parts,i think ans. shld be infinity

bladeX -rise of a new sun

Blazing goIITian

Joined: 12 Dec 2007

Posts: 1249

4 May 2009 13:20:08 IST

Like 0 people liked this

The only impressive answer is given by the expert Anant now tell me suppose u don't know the function log then what is the integration of 1/x........u see what i mean............humans have yet not discovered many functions and constant.............like the discovery of exp(x) is credited to Leonard Euler so who knows one among us discovers this hidden function.

well u an series expansion to approximate just as calculators do..................

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team