GATE 2014 EC (EC2) – Question 55
Evaluate $\int_{-\infty}^{\infty}\operatorname{sinc}^2(5t)\,dt$.
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Show answer and explanation
Correct answer: 0.19 to 0.21
Explanation
Use the normalized communications convention sinc(t)=sin(πt)/(πt), for which ∫sinc²(t)dt=1 by Parseval’s theorem. Substitute u=5t to obtain(1/5)∫sinc²(u)du=**0.2**. The unnormalized sin(t)/t convention would instead giveπ/5, so the official range fixes the intended normalization.