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Homework Help: Math prob

  1. Jul 20, 2005 #1
    v=(1/pi*Ro) integral 20(1-R/Ro)^(1/7) 2*pi*R*dR
    i know that i need to change my variable

    started out y=Ro-R
    dy=-dR

    but havent found a substitution that would get rid of my R variable
     
  2. jcsd
  3. Jul 20, 2005 #2

    HallsofIvy

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    Science Advisor

    ?? R0- R certainly should "get rid of" the R variable. I'm not completely certain whether that first R0 is in the denominator with pi or not. I'll assume it's not.
    What you have is [tex]\frac{20}{\pi}R_0(R_0)^{-\frac{1}{7}}(2\pi)\int(R_0-R)^{\frac{1}{7}}RdR[/tex][tex]=40R_0^{\frac{6}{7}}\int(R_0-R)^{\frac{1}{7}}RdR[/tex].
    Let y= R0- R so that dy= -dR and R= R0- y. Then the integral becomes [tex]-40R_0^{\frac{6}{7}}\int y^{\frac{1}{7}}(R_0-y)dy= -40R_0^{\frac{6}{7}}\int(R_0y^{\frac{1}{7}}- y^{\frac{8}{7}})dy[/tex] which is easy.
     
    Last edited by a moderator: Jul 20, 2005
  4. Jul 20, 2005 #3
    thanks so much!
     
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