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Today's Calculation Of Integral
2005 Today's Calculation Of Integral
69
Today's Calculation of Integral 69
Today's Calculation of Integral 69
Source: 1993 Doshisya University
July 16, 2005
calculus
integration
trigonometry
limit
calculus computations
Problem Statement
Let
f
1
(
x
)
=
x
,
f
n
(
x
)
=
x
+
1
14
∫
0
π
x
f
n
−
1
(
t
)
cos
3
t
d
t
(
n
≥
2
)
f_1(x)=x,f_n(x)=x+\frac{1}{14}\int_0^\pi xf_{n-1}(t)\cos ^ 3 t\ dt\ (n\geq 2)
f
1
(
x
)
=
x
,
f
n
(
x
)
=
x
+
14
1
∫
0
π
x
f
n
−
1
(
t
)
cos
3
t
d
t
(
n
≥
2
)
. Find
lim
n
→
∞
f
n
(
x
)
\lim_{n\to\infty} f_n(x)
lim
n
→
∞
f
n
(
x
)
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