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I need help with an integral 2x dx /(x^2+y^2)^3/2

  • Thread starter astenroo
  • Start date
  • #1
47
0

Homework Statement



I need help with an integral, since my calculus skills aren't the greatest. I need help with getting from this

[tex]\pi[/tex]k[tex]\sigma[/tex]y[tex]\int[/tex] [tex]\frac{2x dx}{(x^{2} + y ^{2})^{3/2}}[/tex] (i)

to this

[tex]\pi[/tex]k[tex]\sigma[/tex]y[tex]\frac{-2}{(x^{2} + y ^{2})^{1/2}}[/tex] (ii)

I integrate from 0 to a (didn't know how to get the limits into TeX in (i) and the gargantuan brackets going on either side in (ii).

Homework Equations





The Attempt at a Solution


Am I supposed to do a substitution here or? In my physics textbook I saw the numerator of (i) written as d(x^2) and the denumerator unchanged as the following step. Now, I believe I have two functions here that i need to integrate 2x and 1/(x^2+y^2)^3/2.
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
From the looks of it, I think they have y2 as constant. So all you need to do is make a substitution like u=x2+y2.
 
  • #3
Delta2
Homework Helper
Insights Author
Gold Member
2,713
852
This is straightforward when u notice that [tex](x^2+y^2)'=2x[/tex]. So just substitute [tex]z=x^2+y^2[/tex] and u ll have [tex]dz=2xdx[/tex] and the integral becomes

[tex]\int z^{-3/2} dz[/tex]
 
  • #4
47
0
Thank you for your replies. I actually managed to solve the integral, but haven't been able to log on to the forum earlier. I did the u substitution and it worked fine fine. Thank you all again for your help!
 

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