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Today's Calculation Of Integral
2010 Today's Calculation Of Integral
656
Today's calculation of Integral 656
Today's calculation of Integral 656
Source:
November 16, 2010
calculus
integration
limit
trigonometry
function
calculus computations
Problem Statement
Find
lim
n
→
∞
n
∫
0
π
2
1
(
1
+
cos
x
)
n
d
x
(
n
=
1
,
2
,
⋯
)
.
\lim_{n\to\infty} n\int_0^{\frac{\pi}{2}} \frac{1}{(1+\cos x)^n}dx\ (n=1,\ 2,\ \cdots).
lim
n
→
∞
n
∫
0
2
π
(
1
+
c
o
s
x
)
n
1
d
x
(
n
=
1
,
2
,
⋯
)
.
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