Topic: Engineering Mathematics
Laplace transform of $t^{2}+2t+3$ is
- A. $\frac{-2}{s^{3}}-\frac{2}{s^{2}}-\frac{3}{s}$
- B. $\frac{2}{s^{3}}+\frac{2}{s^{2}}-\frac{3}{s}$
- C. $\frac{2}{s^{3}}+\frac{2}{s^{2}}+\frac{3}{s}$
- D. $\frac{-2}{s^{3}}+\frac{2}{s^{2}}-\frac{3}{s}$
Answer: C. $\frac{2}{s^{3}}+\frac{2}{s^{2}}+\frac{3}{s}$
Explanation: Using the formula $L(t^{n}) = \frac{n!}{s^{n+1}}$, Laplace transform $L(t^{2}) = \frac{2!}{s^{3}} = \frac{2}{s^{3}}$, $L(2t) = 2 \times \frac{1!}{s^{2}} = \frac{2}{s^{2}}$, and $L(3) = \frac{3}{s}$. Thus, $L(t^{2}+2t+3) = \frac{2}{s^{3}}+\frac{2}{s^{2}}+\frac{3}{s}$.