- #1
thedude36
- 30
- 0
I am having to justify the steps in a proof of the uniqueness theorem. I am supposed to show why the inequality follows from the initial equation.
http://i.imgur.com/AxApogj.png
[itex]\phi[/itex](t) - [itex]\psi[/itex](t) =∫0t 2s[[itex]\phi[/itex](t) - [itex]\psi[/itex](t)] ds
|[itex]\phi[/itex](t) - [itex]\psi[/itex](t)| =|∫0t 2s[[itex]\phi[/itex](t) - [itex]\psi[/itex](t)] ds| [itex]\leq[/itex] ∫0t 2s|[[itex]\phi[/itex](t) - [itex]\psi[/itex](t)]| ds , with t>0
I have no idea where to start. Mostly, I am unsure as to why pulling the 2s out will make it larger than the initial absolute value. Could anyone help?
http://i.imgur.com/AxApogj.png
[itex]\phi[/itex](t) - [itex]\psi[/itex](t) =∫0t 2s[[itex]\phi[/itex](t) - [itex]\psi[/itex](t)] ds
|[itex]\phi[/itex](t) - [itex]\psi[/itex](t)| =|∫0t 2s[[itex]\phi[/itex](t) - [itex]\psi[/itex](t)] ds| [itex]\leq[/itex] ∫0t 2s|[[itex]\phi[/itex](t) - [itex]\psi[/itex](t)]| ds , with t>0
I have no idea where to start. Mostly, I am unsure as to why pulling the 2s out will make it larger than the initial absolute value. Could anyone help?