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Today's Calculation Of Integral
2007 Today's Calculation Of Integral
176
Today's calculation of Integral 176
Today's calculation of Integral 176
Source: Gunma University entrance exam 1969
February 4, 2007
calculus
integration
trigonometry
limit
induction
symmetry
calculus computations
Problem Statement
Let
f
n
(
x
)
=
∑
k
=
1
n
sin
k
x
k
(
k
+
1
)
.
f_{n}(x)=\sum_{k=1}^{n}\frac{\sin kx}{\sqrt{k(k+1)}}.
f
n
(
x
)
=
∑
k
=
1
n
k
(
k
+
1
)
s
i
n
k
x
.
Find
lim
n
→
∞
∫
0
2
π
{
f
n
(
x
)
}
2
d
x
.
\lim_{n\to\infty}\int_{0}^{2\pi}\{f_{n}(x)\}^{2}dx.
lim
n
→
∞
∫
0
2
π
{
f
n
(
x
)
}
2
d
x
.
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