Discussion
Laplace transform of (1 + sin (2t)) is :
Answer: B
The transform is \(\frac{1}{s} + \frac{2}{s^{2} + 4}\).
The Laplace transform is linear, so transform each term:
\[ \begin{aligned} \mathcal{L}\{1\} &= \frac{1}{s} \\ \mathcal{L}\{\sin at\} &= \frac{a}{s^{2} + a^{2}}, \quad a \\ &= 2 \\ \mathcal{L}\{1 + \sin 2t\} &= \frac{1}{s} + \frac{2}{s^{2} + 4} \end{aligned} \]
\(\frac{1}{s^{2} + 1}\) uses \(a = 1\); \(\frac{4s}{s^{2} + 4}\) confuses the sine with the cosine transform \(\frac{s}{s^{2} + a^{2}}\); and the option starting with 1 forgets that \(\mathcal{L}\{1\} = \frac{1}{s}\).
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