The variables t and x are related by t = x+√(x^2+2bx+c) where b and c are constants and
b^2<c. Show that
dx/dt=(t-x)/(t+b)
and hence integrate
1/√(x^2+2bx+c)
Verify by direct integration that your result holds also in the case b^2 = c if x+b > 0 but that
your result does not hold in the case b^2 = c if x + b < 0 .
[and come someone tell me how to use the math symbols at this site.. i had to do everything in microsoft word ]
Hello iPod
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and hence integrate
1/√(x^2+2bx+c)
, provided
Can you finish up?
Grandad
PSThe language is called LaTeX, and you'll find some help on this site here: http://www.mathhelpforum.com/math-help/latex-help/[and come someone tell me how to use the math symbols at this site.. i had to do everything in microsoft word ]
I also find the Wikipedia site helpful, here: LaTeX/Mathematics - Wikibooks, collection of open-content textbooks
When you've written some LaTex code, select what you've written and click the button on this editor's toolbar, and the editor will insert [tex]...[/tex] tags around the selection. Use 'Preview Changes' to check that it's OK.
To see any of the code I've used in my solution above, just click-left on any line and the code will appear in a separate pop-up window. Go on, try it now!
Grandad
Oh yeah , it is known as Euler's substitution for integration .
We can solve integrals in this form using Euler's substitution
Therefore , the integral becomes
Then , what does f(t) refer to ?
Since
For more details , you can take a look at http://planetmath.org/encyclopedia/E...tegration.html .
Euler's substitution is a powerful tools indeed . Make use of it !!