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

Integral Calculus

Cool goIITian

Joined:	14 Jan 2007
Post:	50

3 Nov 2007 00:56:24 IST

0 People liked this

596

Is the given function integrable?

None

^{[ (cos x - sin x)/}

(sin x) dx

Share this article on:

Comments (7)

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

3 Nov 2007 01:25:55 IST

Like 1 people liked this

It is non-integrable.

kousik_paul

Cool goIITian

Joined: 14 Jan 2007

Posts: 50

3 Nov 2007 05:57:18 IST

Like 0 people liked this

Bipin,
why the functionis non integrable?

astrojith

Blazing goIITian

Joined: 5 Jun 2007

Posts: 336

8 Nov 2007 20:28:14 IST

Like 0 people liked this

It can be integrated (I think). Here's my attempt :

(cosx-sinx) / (

sinx) dx

Let I₁=

(cosx) /

sinx dx
Let I₂=

(sinx) /

sinx dx

Integrating I₁Take sinx = t² ; cosxdx = 2tdt

I₁=

2t/t dt = 2

dt = 2t = 2sinx

Integrating I₂Take sinx = t² ; cosxdx = 2tdt ; dx = (2tdt) / cosx

I₂=

(sinx) /

sinx dx = 2

(t³) / [t(1-t²)] dt = 2

t² / (1-t²)

= -4t - log|t-1/t+1| = -4sinx - log|sinx-1/sinx+1| + C

I've skipped some steps here since they are less significant.

Result

I₁+I₂= 2sinx - 4sinx - log|sinx-1/sinx+1| +C
= -2sinx - log|sinx-1/sinx+1| + C

There it is. Its the answer. I can't understand why its non-integrable. But its just my humble attempt. Someone please confirm it.

If you think its right, please rate me. :)

Aditya Arora

Blazing goIITian

Joined: 3 Dec 2006

Posts: 1043

8 Nov 2007 20:43:12 IST

Like 0 people liked this

Yeah, i too think its integrable. Same way as astrojith

Nadeem

Blazing goIITian

Joined: 25 Aug 2007

Posts: 521

8 Nov 2007 20:45:22 IST

Like 0 people liked this

@astrojith,
pls check these lines in ur answer , I think they r wrong

>Integrating I₂>Take sinx = t² ; cosxdx = 2tdt ; dx = (2tdt) / cosx

>I₂=

(sinx) /

sinx dx = 2

(t³) / [t(1-t²)] dt = 2

t² / (1-t²)

cosx =

( 1- t⁴) .
u have taken it as (

( 1- t²) )²

But I'm not sure whether its integrable or not.

astrojith

Blazing goIITian

Joined: 5 Jun 2007

Posts: 336

9 Nov 2007 22:21:05 IST

Like 0 people liked this

@ nadeemoidu : Good point man. I didn't notice it. Anyway, isn't it integratable ? I can't understand why its not.

RAKESH KUMAR

Cool goIITian

Joined: 24 Mar 2007

Posts: 39

10 Nov 2007 20:19:08 IST

Like 0 people liked this

YES, THIS FUNCTION IS INTEGRABLE.
I WILL SOLVE THIS QUESTION AS SOON AS POSSIBLE,
SINCE I AM BUSY RIGHT NOW

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