I am struggling to solve this problem: $$I=\int_{-\infty}^\infty (t^2+\cos (\pi t))\delta(t-1) dt $$ in System and Signals. I saw a formula in the internet. Is it solved by this formula?
2026-04-03 21:40:29.1775252429
How to solve this problem with Dirac Delta function?
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Integrating a function $f(t)$ against the delta function $t \mapsto \delta(t-1)$ corresponds to evaluating $f(1)$. In our case, this is $1^2 + \cos \pi 1 = 0$. If this seems strange or magical to you, that's good. There's a lot of subterfuge and sophistication involved here.