WBJEE · Maths · Definite Integration
If \(\phi(t)=\left\{\begin{array}{l}1, \text { for } 0 \leq t < 1 \\ 0, \text { otherwise }\end{array},\right.\) then \(\int_{-3000}^{3000}\left(\sum_{r^{\prime}=2014}^{2016} \phi(t-r') \phi(t-2016)\right) d t\) is
- A a real number
- B 1
- C 0
- D does not exist
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
\(\int_{-3000}^{3000}\left(\sum_{r'=2014}^{2016} \phi\left(t-r^{\prime}\right) \phi(t-2016)\right) d t\) \(=\int_{-3000}^{3000}[\phi(t-2014) \phi(t-2016)+\phi(t-2015) \phi(t-2016) +\phi(t-2016) \phi(t-2016)] \mathrm{dt}\)…
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