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Mathematics
Mathematics
Problem
If
I
m
,
n
=
∫
cos
m
x
⋅
cos
n
x
d
x
I_{m,n} = \int \cos^m x \cdot \cos nx \, dx
I
m
,
n
=
∫
cos
m
x
⋅
cos
n
x
d
x
, show that
(
m
+
n
)
I
m
,
n
=
cos
m
x
⋅
sin
n
x
+
m
I
(
m
−
1
,
n
−
1
)
(m+n) I_{m,n} = \cos^m x \cdot \sin nx + m I_{(m-1,n-1)}
(
m
+
n
)
I
m
,
n
=
cos
m
x
⋅
sin
n
x
+
m
I
(
m
−
1
,
n
−
1
)
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