Question

Help with unit impulse function

Answer 1

\[\int\limits_{-2}^{3}\frac{ t+1 }{ t^2+1} \delta(5t - 5) dt \]

Answer 2

Using two properties of the unit impulse function I was able to reduce the integral to
\[\frac{ 1 }{ 5 }\int\limits_{-2}^{3} (1) \delta(t-1)dt\]

Answer 3

My question is : Because property ii that states that , (see attached image )

Answer 4

Does that mean that the unit step functions integral's limit describe an enclosed area - So the properties allows that the integral above to evaluates to 1