Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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(Sifting property of impulse)

(a) Evaluate the integral \(\int_{-3}^{5} \left( 10\delta(t + 4) + 4\delta(t - 1) + 3\delta(t + 5.05) \right) dt\).

(b) Evaluate the integral \(\int_{-\infty}^{\infty} \left( (t^3 - t)\delta(t + 2) + t^2 \delta(t - 3) \right) \cos(\pi t) dt\).

(c) Find and sketch the function

\[ s(t) = \int_{-\infty}^{t-2} 6\delta(\tau + 3) d\tau \]

for \(-\infty < t < \infty\).
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Transcribed Image Text:(Sifting property of impulse) (a) Evaluate the integral \(\int_{-3}^{5} \left( 10\delta(t + 4) + 4\delta(t - 1) + 3\delta(t + 5.05) \right) dt\). (b) Evaluate the integral \(\int_{-\infty}^{\infty} \left( (t^3 - t)\delta(t + 2) + t^2 \delta(t - 3) \right) \cos(\pi t) dt\). (c) Find and sketch the function \[ s(t) = \int_{-\infty}^{t-2} 6\delta(\tau + 3) d\tau \] for \(-\infty < t < \infty\).
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