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Mathematics
Mathematics
Problem
If
m
,
n
∈
N
m, n \in N
m
,
n
∈
N
, then
I
m
,
n
=
∫
0
1
x
m
(
1
−
x
)
n
d
x
I_{m,n} = \int_{0}^{1} x^m (1-x)^n dx
I
m
,
n
=
∫
0
1
x
m
(
1
−
x
)
n
d
x
is equal to a.
m
!
n
!
(
m
+
n
+
2
)
!
\frac{m! n!}{(m+n+2)!}
(
m
+
n
+
2
)!
m
!
n
!
b.
2
m
!
n
!
(
m
+
n
+
1
)
!
\frac{2m! n!}{(m+n+1)!}
(
m
+
n
+
1
)!
2
m
!
n
!
c.
m
!
n
!
(
m
+
n
+
1
)
!
\frac{m! n!}{(m+n+1)!}
(
m
+
n
+
1
)!
m
!
n
!
d. None of these
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