Question

Just (d)

1-26. Evaluate the following integrals. .10 (a) | cos 2nt δ(1-2) dt (b) | cos 2nt δ(1-2) dt (c) | cos 2nt δ(t-0.5) dt (d) (t 2)82) dt (e)S 2) dr Al

Answer 1

δ(t) is called unit impulse function or dirac delta function.

Its is 0 for all values except t=0.

at t=0 its not defined.

See the fig.

delta (t) is called unit impulse function or dirac delta function. Its is 0 for all values except t = 0. at t = 0 its not defined. See the fig. integral^infinity_-infinity f (t) delta (t - tau) = f (tau) integral^infinity_-infinity (t - 2)^2 delta (t - 2) dt here f (t) = (t - 2)^2 tau = 2 So integral^infinity_-infinity (t - 2)^2 delta (t - 2) dt = f (2) = (2 - 2)^2 = 0

Ans 0.