Pilihan Topik Matematika - at ee-cafe.org
Pilihan Topik Matematika - at ee-cafe.org
Pilihan Topik Matematika - at ee-cafe.org
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269<br />
⎥<br />
⎦<br />
⎤<br />
⎢<br />
⎣<br />
⎡<br />
τ<br />
− τ<br />
τ<br />
=<br />
⎥<br />
⎦<br />
⎤<br />
⎢<br />
⎣<br />
⎡<br />
τ<br />
− τ<br />
τ<br />
= ∫<br />
∫ ∫<br />
∞<br />
−<br />
t<br />
st<br />
t<br />
d<br />
t<br />
f<br />
f<br />
dt<br />
e<br />
d<br />
t<br />
f<br />
f<br />
s<br />
F<br />
s<br />
F<br />
0<br />
2<br />
1<br />
0 0<br />
2<br />
1<br />
2<br />
1 )<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
( L<br />
CONTOH: Carilah f(t) dari F(s) berikut.<br />
)<br />
(<br />
1<br />
)<br />
(<br />
c).<br />
)<br />
)(<br />
(<br />
1<br />
)<br />
(<br />
b).<br />
)<br />
(<br />
1<br />
)<br />
(<br />
a).<br />
2<br />
2<br />
a<br />
s<br />
s<br />
s<br />
F<br />
b<br />
s<br />
a<br />
s<br />
s<br />
F<br />
a<br />
s<br />
s<br />
F<br />
+<br />
=<br />
+<br />
+<br />
=<br />
+<br />
=<br />
Solusi : a). Fungsi ini kita pandang sebagai perkalian dari dua<br />
fungsi.<br />
<strong>at</strong><br />
t<br />
<strong>at</strong><br />
t<br />
ax<br />
<strong>at</strong><br />
ax<br />
t<br />
x<br />
t<br />
a<br />
ax<br />
t<br />
<strong>at</strong><br />
te<br />
dx<br />
e<br />
dx<br />
e<br />
dx<br />
e<br />
e<br />
dx<br />
x<br />
t<br />
f<br />
x<br />
f<br />
t<br />
f<br />
e<br />
t<br />
f<br />
t<br />
f<br />
a<br />
s<br />
s<br />
F<br />
s<br />
F<br />
s<br />
F<br />
s<br />
F<br />
s<br />
F<br />
−<br />
−<br />
+<br />
−<br />
−<br />
−<br />
−<br />
−<br />
−<br />
=<br />
=<br />
=<br />
=<br />
−<br />
=<br />
⇒<br />
=<br />
=<br />
→<br />
+<br />
=<br />
=<br />
=<br />
∫<br />
∫<br />
∫<br />
∫<br />
0<br />
0<br />
0<br />
)<br />
(<br />
0<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
1<br />
)<br />
(<br />
)<br />
(<br />
dengan<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
b). Fungsi ini juga merupakan perkalian dari dua fungsi.<br />
bt<br />
<strong>at</strong><br />
e<br />
t<br />
f<br />
e<br />
t<br />
f<br />
b<br />
s<br />
s<br />
F<br />
a<br />
s<br />
s<br />
F<br />
s<br />
F<br />
s<br />
F<br />
s<br />
F<br />
−<br />
−<br />
=<br />
=<br />
→<br />
+<br />
=<br />
+<br />
=<br />
=<br />
)<br />
(<br />
dan<br />
)<br />
(<br />
)<br />
(<br />
1<br />
)<br />
(<br />
dan<br />
)<br />
(<br />
1<br />
)<br />
(<br />
dengan<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
2<br />
1<br />
2<br />
1<br />
2<br />
1<br />
( )<br />
b<br />
a<br />
e<br />
e<br />
b<br />
a<br />
e<br />
e<br />
b<br />
a<br />
e<br />
e<br />
dx<br />
e<br />
e<br />
dx<br />
e<br />
e<br />
dx<br />
x<br />
t<br />
f<br />
x<br />
f<br />
t<br />
f<br />
bt<br />
<strong>at</strong><br />
t<br />
b<br />
a<br />
bt<br />
t<br />
x<br />
b<br />
a<br />
bt<br />
t<br />
x<br />
b<br />
a<br />
bt<br />
t<br />
x<br />
t<br />
b<br />
ax<br />
t<br />
+<br />
−<br />
−<br />
=<br />
+<br />
−<br />
−<br />
=<br />
⎥<br />
⎥<br />
⎦<br />
⎤<br />
⎢<br />
⎢<br />
⎣<br />
⎡<br />
+<br />
−<br />
=<br />
=<br />
=<br />
−<br />
=<br />
⇒<br />
−<br />
−<br />
+<br />
−<br />
−<br />
+<br />
−<br />
−<br />
+<br />
−<br />
−<br />
−<br />
−<br />
−<br />
∫<br />
∫<br />
∫<br />
1<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
0<br />
)<br />
(<br />
0<br />
)<br />
(<br />
0<br />
)<br />
(<br />
0<br />
2<br />
1