Question:
Consider a continuous-time signal
\[
x(t) = -t^2 \left\{ u(t+4) - u(t-4) \right\}
\]
where \( u(t) \) is the continuous-time unit step function. Let \( \delta(t) \) be the continuous-time unit impulse function. The value of
\[
\int_{-\infty}^{\infty} x(t)\delta(t+3) \, dt
\]
is:
Consider a continuous-time signal
\[
x(t) = -t^2 \left\{ u(t+4) - u(t-4) \right\}
\]
where \( u(t) \) is the continuous-time unit step function. Let \( \delta(t) \) be the continuous-time unit impulse function. The value of
\[
\int_{-\infty}^{\infty} x(t)\delta(t+3) \, dt
\]
is:
Show Hint
To evaluate \( \int x(t)\delta(t+a)\,dt \), apply the sifting property: it equals \( x(-a) \). Ensure that the value lies within the domain where \( x(t) \) is defined and non-zero.
Updated On: Feb 3, 2026
- \( -9 \)
- \( 9 \)
- \( 3 \)
- \( -3 \)
Show Solution
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The Correct Option is A
Solution and Explanation
We use the sifting property of the Dirac delta function:
=
Now evaluate \( x(-3) \). The signal \( x(t) \) is defined as:
-9 in
=
Now evaluate \( x(-3) \). The signal \( x(t) \) is defined as:
-9 in
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