演習問題5.3.1

1.: 次の関数のラプラス変換を求めよ．
(a): $\displaystyle{ t^2 + 3t - 4}$
(b): $\displaystyle{ e^{3t +4}}$
(c): $\displaystyle{ \sin^{2}{t}}$
(d): $\displaystyle{ e^{2t}\sin{t}}$
(e): $\displaystyle{ t^{3}e^{3t}}$
(f): $\displaystyle{ \cos{(t+a)}}$
(g): $\displaystyle{ \left\{\begin{array}{rl} 2,&0 < t < 3\\ 0,&3 < t < 6\\ 2,&t > 6 \end{array} \right.}$
(h): $\displaystyle{ \left\{\begin{array}{rl} 0,&0 < t < \frac{\pi}{2}\\ \sin{t},&t > \frac{\pi}{2} \end{array} \right. }$
(i): $\displaystyle{ \left\{\begin{array}{rl} 2,& 0 < t < 2\\ t^2,& 2 < t < 4\\ t,& 4 < t < 8\\ 3,& t > 8 \end{array}\right. }$