GATE 2022 ES – Question 13
For s>0, find the Laplace transform of $f(x)=\sin(ax)$.
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Correct answer: (A) $a/(s^2+a^2)$
Explanation
Integrate $\int_0^\infty e^{-sx}\sin(ax)\,dx$, or take the imaginary part of $1/(s-ia)$. Rationalization gives imaginary part $a/(s^2+a^2)$. Thus **A**. The corresponding cosine transform has numerator s.