(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Integrate the following by parts twice

[itex]\int_{a}^{b}\frac{d}{dr}(r\frac{dT(r)}{dr})\psi(r)dr[/itex]

and show that it can be written as [itex]-\lambda^2\bar{T}[/itex] , where

[itex]\bar{T}=\int_{a}^{b}r\psi(r)T(r)dr[/itex]

and the function [itex]\psi[/itex] satisfies the following equation

[itex]\frac{1}{r}\frac{d}{dr}(r\frac{d\psi(r)}{dr})+\lambda^2\psi(r)=0[/itex]

Relevant equations and attempt

Of course the integration by parts equation, but I used the tabular method to get the first integration of:

[itex]\psi(r)r\frac{dT(r)}{dr}-\int_{a}^{b}\psi\prime(r)r\frac{dT(r)}{dr}dr[/itex]

But as you can see in the next step it gets more complicated because the v choice now needs integration by parts as well and since the T(r) portion will end up being an integral without a definite solution, I don't know where to take it from there. I tried to get things to cancel but haven't found a way yet. Am I going about this the wrong way?

On the second integration by parts I tried to group [itex]\psi\prime(r)r[/itex] together under u and it cleaned up v, but u became a mess without a way to cancel.

Any help would be greatly appreciated. I am a little rusty on this stuff and this was provided as a refresher problem to me.

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# Homework Help: Advance Integration By Parts

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