ISRO Electronics & Communication (ECE) 2008 - Question 47

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Topic: Signals and Systems

Evaluate the function $\int_{0}^{\infty}t^{2}\delta(t-3)dt$

  • A. $e^{-t^{2}}$
  • B. $\frac{t^{3}}{3}$
  • C. $t^{2}(t-3)$
  • D. 9

Answer: D. 9

Explanation: $I=\int_{0}^{\infty}t^{2}\delta(t-3)dt=3^{2}=9;$ at $t=3$ $=0$; otherwise

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