Question

The Laplace transform of the function 10 + 5t + t^2 – 4t^3 is ___________

(a) \(\frac{10}{s} + \frac{5}{s^2}  + \frac{2}{s^3}  – \frac{24}{s^4}\)

(b) \(\frac{10}{s} – \frac{5}{s^2}  + \frac{2}{s^3}  – \frac{24}{s^4}\)

(c) \(\frac{10}{s} – \frac{5}{s^2}  – \frac{2}{s^3}  – \frac{24}{s^4}\)

(d) \(\frac{10}{s} + \frac{5}{s^2}  + \frac{2}{s^3}  + \frac{24}{s^4}\)

I have been asked this question in examination.

Question is taken from Common Laplace Transforms in section Laplace Transform and System Design of Signals and Systems

Answer 1

Right choice is (a) \(\frac{10}{s} + \frac{5}{s^2}  + \frac{2}{s^3}  – \frac{24}{s^4}\)

To explain I would say: L {10 + 5t + t^2 – 4t^3} = \(\frac{10}{s} + \frac{5}{s^2}  + \frac{2}{s^3}  – \frac{4 3!}{s^4}\)

= \(\frac{10}{s} + \frac{5}{s^2}  + \frac{2}{s^3}  – \frac{24}{s^4}\).