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If , then is equal…
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
If
m
,
n
∈
N
m,n\in\mathbb{N}
m
,
n
∈
N
, then
I
m
,
n
=
∫
0
1
x
m
(
1
−
x
)
n
d
x
I_{m,n}=\int_0^1x^m(1-x)^n\,dx
I
m
,
n
=
∫
0
1
x
m
(
1
−
x
)
n
d
x
is equal to (1)
m
!
n
!
(
m
+
n
+
2
)
!
\frac{m!n!}{(m+n+2)!}
(
m
+
n
+
2
)!
m
!
n
!
(2)
2
m
!
n
!
(
m
+
n
+
1
)
!
\frac{2m!n!}{(m+n+1)!}
(
m
+
n
+
1
)!
2
m
!
n
!
(3)
m
!
n
!
(
m
+
n
+
1
)
!
\frac{m!n!}{(m+n+1)!}
(
m
+
n
+
1
)!
m
!
n
!
(4) None of these
Related theory
Integration by Parts
Integration Techniques
Integrals
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