Math prob

  • Thread starter jennypear
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  • #1
jennypear
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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
 

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  • #2
HallsofIvy
Science Advisor
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?? 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.
 
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  • #3
jennypear
16
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thanks so much!
 

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