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Mathematics
Mathematics
Problem
The option(s) with the values of
a
a
a
and
L
L
L
that satisfy the equation
∫
0
4
π
e
t
(
sin
6
a
t
+
cos
4
a
t
)
d
t
∫
0
π
e
t
(
sin
6
a
t
+
cos
4
a
t
)
d
t
=
L
\frac{\int_0^{4\pi} e^t (\sin^6 at + \cos^4 at)\,dt}{\int_0^{\pi} e^t (\sin^6 at + \cos^4 at)\,dt} = L
∫
0
π
e
t
(
sin
6
a
t
+
cos
4
a
t
)
d
t
∫
0
4
π
e
t
(
sin
6
a
t
+
cos
4
a
t
)
d
t
=
L
is/are: a.
a
=
2
,
L
=
e
4
π
−
1
e
π
−
1
a = 2, L = \frac{e^{4\pi} - 1}{e^\pi - 1}
a
=
2
,
L
=
e
π
−
1
e
4
π
−
1
b.
a
=
2
,
L
=
e
4
π
+
1
e
π
+
1
a = 2, L = \frac{e^{4\pi} + 1}{e^\pi + 1}
a
=
2
,
L
=
e
π
+
1
e
4
π
+
1
c.
a
=
4
,
L
=
e
4
π
−
1
e
π
−
1
a = 4, L = \frac{e^{4\pi} - 1}{e^\pi - 1}
a
=
4
,
L
=
e
π
−
1
e
4
π
−
1
d.
a
=
4
,
L
=
e
4
π
+
1
e
π
+
1
a = 4, L = \frac{e^{4\pi} + 1}{e^\pi + 1}
a
=
4
,
L
=
e
π
+
1
e
4
π
+
1
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