Solution 2.9.2.4
f(t)=t[1(t;T); 1(t;2T)]
Then
F(s) = Lf(t;T)1(t; T)+T1(t; T)g;Lf(t ;2T)1(t;2T)+2T1(t;2T)g
= Lf(t;T)1(t; T)g+ Lf(T1(t;T)g;Lf(t; 2T)1(t; 2T)g;Lf2T1(t; 2T)g
=
e
;Ts
s
2
+
Te
;Ts
s
;
e
;2Ts
s
2
;
2Te
;2Ts
s
=
e
;Ts
+ Tse
;Ts
; e
;2Ts
; 2Te
;2Ts
s
2
1