Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Calculus of Variations Variation of a Functional
For any two continuous functions f, g : ℝ → ℝ, define
\(\displaystyle f ⋆ g(t)=\int_0^t f(s) g(t-s) d s .\)
Which of the following is the value of f ⋆ g(t) when f(t) = exp(-t) and g(t) = sin(t)?
1
\(\frac{1}{2}[\exp (-t)+\sin (t)-\cos (t)]\).
2
\(\frac{1}{2}[-\exp (-t)+\sin (t)-\cos (t)] \).
3
\(\frac{1}{2}[\exp (-t)-\sin (t)-\cos (t)] \).
4
\(\frac{1}{2}[\exp (-t)+\sin (t)+\cos (t)] \).
5
Question Not Attempted