Ejercicios de repaso sección 4.7
Resolver la transformada de integrales
L
{
1
∗
t
3
}
\hspace{0.5cm} \mathscr{L}\left\{1\ast t^3\right\}
L
{
1
∗
t
3
}
L
{
t
2
∗
t
e
t
}
\hspace{0.5cm} \mathscr{L}\left\{t^2\ast t e^t\right\}
L
{
t
2
∗
t
e
t
}
L
{
e
−
t
∗
e
t
c
o
s
t
}
\hspace{0.5cm} \mathscr{L}\left\{e^{-t}\ast e^tcos{t}\right\}
L
{
e
−
t
∗
e
t
cos
t
}
L
{
e
2
t
∗
s
e
n
t
}
\hspace{0.5cm} \mathscr{L}\left\{e^{2t}\ast sen{t}\right\}
L
{
e
2
t
∗
se
n
t
}
L
{
∫
0
t
e
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{\int_{0}^{t}{e^\tau d\tau}\right\}
L
{
∫
0
t
e
τ
d
τ
}
L
{
∫
0
t
c
o
s
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{\int_{0}^{t}{cos{\tau}d\tau}\right\}
L
{
∫
0
t
cos
τ
d
τ
}
L
{
∫
0
t
e
−
τ
c
o
s
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{\int_{0}^{t}{e^{-\tau}cos{\tau}d\tau}\right\}
L
{
∫
0
t
e
−
τ
cos
τ
d
τ
}
L
{
∫
0
t
τ
s
e
n
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{\int_{0}^{t}\tau sen\tau d\tau\right\}
L
{
∫
0
t
τ
se
n
τ
d
τ
}
L
{
∫
0
t
τ
e
t
−
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{\int_{0}^{t}{\tau e^{t-\tau}d\tau}\right\}
L
{
∫
0
t
τ
e
t
−
τ
d
τ
}
L
{
∫
0
t
s
e
n
τ
c
o
s
(
t
−
τ
)
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{\int_{0}^{t}{sen\tau c o s{(}t-\tau)d\tau}\right\}
L
{
∫
0
t
se
n
τ
cos
(
t
−
τ
)
d
τ
}
L
{
t
∫
0
t
s
e
n
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{t\int_{0}^{t}sen\tau d\tau\right\}
L
{
t
∫
0
t
se
n
τ
d
τ
}
L
{
t
∫
0
t
τ
e
−
τ
d
τ
}
\hspace{0.5cm} \mathscr{L}\left\{t\int_{0}^{t}{\tau e^{-\tau}d\tau}\right\}
L
{
t
∫
0
t
τ
e
−
τ
d
τ
}