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Today's Calculation Of Integral
2008 Today's Calculation Of Integral
380
Today's calculation of Integral 380
Today's calculation of Integral 380
Source: 1997 Hukui Medical College entrance exam
October 18, 2008
calculus
integration
calculus computations
Problem Statement
Find
∫
−
1
1
(
n
k
)
(
1
+
x
)
n
−
k
(
1
−
x
)
k
d
x
(
k
=
0
,
1
,
2
,
⋯
n
)
\int_{ - 1}^1 {n\choose k}(1 + x)^{n - k}(1 - x)^k\ dx\ (k = 0,\ 1,\ 2,\ \cdots n)
∫
−
1
1
(
k
n
)
(
1
+
x
)
n
−
k
(
1
−
x
)
k
d
x
(
k
=
0
,
1
,
2
,
⋯
n
)
.
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