Integrating the following delta dirac function should yield min(t,s), but how?

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SUMMARY

The integration of the delta Dirac function, represented as ∫₀ᵗ∫₀ˢ δ(τ-τ') dτ dτ', yields the result min(t,s). To solve this, it is essential to analyze the cases where s > t and s < t separately. By changing the order of integration, one can directly compute the integral, confirming the result.

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Bablo
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Homework Statement


I need to understand how to integrate
[tex]\int_{0}^{t}\int_{0}^{s} \delta(\tau-\tau')d\tau d\tau'[/tex]
The solution is [tex]min(t,s)[/tex]

Homework Equations


See above

The Attempt at a Solution


[tex]min(t,s)[/tex]
 
Last edited:
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hey Bablo

have you tried considering each of the cases separately (s>t,s<t)? then you can change the order of integration and integrate directly...
 

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