My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
January 16th, 2013, 09:38 AM   #1
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

integrals

[color=#0000FF]Dear All!
Please, does anyone have an idea how to solve:

the result is ment to be:

Many thanks!
[/color]
ungeheuer is offline  
 
January 16th, 2013, 10:26 AM   #2
Math Team
 
zaidalyafey's Avatar
 
Joined: Aug 2012
From: Sana'a , Yemen

Posts: 1,177
Thanks: 44

Math Focus: Theory of analytic functions
Re: integrals

Use the substitution t = arcsin(x) ,
zaidalyafey is offline  
January 16th, 2013, 09:25 PM   #3
Newbie
 
Joined: Jan 2013

Posts: 13
Thanks: 0

Re: integrals

Interesting problem. It's just a u-sub as zaida mentioned.

Split the into if you don't see the cancelling.

Jc
jc90usa is offline  
January 19th, 2013, 07:57 AM   #4
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: integrals

[color=#0000FF]Thank you!
now I have the integral of a rational function!



what now?
http://integral-table.com/integral-tabl ... 0000000000
nth frm this goes well with...???


[/color]
ungeheuer is offline  
January 20th, 2013, 02:54 PM   #5
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: integrals

Quote:
Originally Posted by ungeheuer
[color=#0000FF][b]Thank you!
now I have the integral of a rational function!

[color=#000000]
Nonsense! For one thing this is NOT a rational function because it involves square roots. Second, you do not have a "dx" or "du", necessary for an integral. Third, you have both "x" and "u" in the integral- you must have one or the other (depending upon whether you have "dx" or "du") not both.

What you had originally was and the substitution was suggested. But you can't just replace the one instance of arcsin(x) by u and leave the rest of the integral alone. You will have to replace "dx" with something involving only "u" and "du". To get "dx" and "du", of course, you will need to take the derivative. What is the derivative of arcsin(x)?[/color]

Quote:
[color= #0000FF] what now?
http://integral-table.com/integral-tabl ... 0000000000
nth frm this goes well with...???


[/color]
HallsofIvy is offline  
January 21st, 2013, 06:16 AM   #6
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: integrals

[color=#0000FF]Thank U, HallsofIvvy!
(Well, be honest and admit it is not that easy!)

[/color]
ungeheuer is offline  
January 21st, 2013, 06:28 AM   #7
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,958
Thanks: 1146

Math Focus: Elementary mathematics and beyond
Re: integrals







greg1313 is offline  
January 21st, 2013, 06:37 AM   #8
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: integrals

[color=#0000FF]
I dont get this...
we dont know what is cosy?
how do we know that it is 1?
[/color]
ungeheuer is offline  
January 23rd, 2013, 10:14 AM   #9
Senior Member
 
Joined: Oct 2012

Posts: 460
Thanks: 0

Re: integrals

[color=#0000FF]Hello!
Now I have:



what shoud I do now?
many thanks!

Not finding the idea at:
http://integral-table.com/

[/color]
ungeheuer is offline  
January 23rd, 2013, 01:20 PM   #10
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: integrals

I believe you have done this same thing repeatedly and been told, repeatedly, that you cannot do it! You cannot replace part of the function so that it is in terms of "u" while leaving the rest in terms of "x".

That was the whole point in suggesting the substitution u= arcsin(x). Differentiating both sides, . You have put that in backwards, writing it as if it were . Instead write the integral as .
HallsofIvy is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
integrals



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
integrals ungeheuer Calculus 10 July 21st, 2013 03:30 AM
Integrals veronicak5678 Real Analysis 1 May 1st, 2012 12:25 PM
integrals damar10 Calculus 1 April 25th, 2012 08:34 AM
Integrals johnnyboy20 Calculus 2 May 24th, 2011 04:36 PM
integrals hector manuel Real Analysis 0 May 4th, 2009 11:16 PM





Copyright © 2019 My Math Forum. All rights reserved.