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

Integral Calculus

New kid on the Block

Joined:	3 Nov 2007
Post:	1

3 Nov 2007 23:10:06 IST

0 People liked this

398

dx/(x-a)(x-b)

None

dx/(x-a)(x-b)

Share this article on:

Comments (3)

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

3 Nov 2007 23:19:12 IST

Like 1 people liked this

Fro such types of questions use partial fractions.

Write 1/(x-a)(x-b) = A/(x-a) + B/(x-b)

Multiply both sides by (x-a)(x-b) :

1 = A(x-b) + B(x-a)

Now put x=a you'll get A = 1/(a-b)

Put x=b you'll get B = 1/(b-a) = -1/(a-b)

so 1/(x-a)(x-b) = {1/(a-b)}.{1/(x-a) - 1/(x-b)}

the given integral reduces to

I =

{1/(a-b)}.{1/(x-a) - 1/(x-b)}.dx

I = {1/(a-b)}.{ln|x-a| - ln|x-b|} + c

I = {1/(a-b)}.{ln(|x-a|/|x-b|)} + c

Krishna Gopal Singh

Forum Expert

Joined: 29 Dec 2006

Posts: 5153

3 Nov 2007 23:26:35 IST

Like 0 people liked this

Let 1/(x-a)(x-b)=A/(x-a)+B/(x-b)
By equating coefficient's
A+B=0
Ab+aB=1
A=1/(b-a), B=1/(a-b)
So integral is
(1/(b-a))*ln((x-a)/(x-b))

kousik_paul

Cool goIITian

Joined: 14 Jan 2007

Posts: 50

4 Nov 2007 00:44:31 IST

Like 0 people liked this

1/root(x^2-(a+b)x+ab
1/root{(x-(a+b)/2)^2-((a-b)/2)^2
so answer is
log(mod(x-(a+b)/2+root((x-a)*(x-b)}

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