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Today's Calculation Of Integral
2010 Today's Calculation Of Integral
649
Today's calculation of Integral 649
Today's calculation of Integral 649
Source:
September 20, 2010
calculus
integration
trigonometry
limit
calculus computations
Problem Statement
Let
f
n
(
x
,
y
)
=
n
r
cos
π
r
+
n
2
r
3
(
r
=
x
2
+
y
2
)
f_n(x,\ y)=\frac{n}{r\cos \pi r+n^2r^3}\ (r=\sqrt{x^2+y^2})
f
n
(
x
,
y
)
=
r
c
o
s
π
r
+
n
2
r
3
n
(
r
=
x
2
+
y
2
)
,
I
n
=
∫
∫
r
≤
1
f
n
(
x
,
y
)
d
x
d
y
(
n
≥
2
)
.
I_n=\int\int_{r\leq 1} f_n(x,\ y)\ dxdy\ (n\geq 2).
I
n
=
∫
∫
r
≤
1
f
n
(
x
,
y
)
d
x
d
y
(
n
≥
2
)
.
Find
lim
n
→
∞
I
n
.
\lim_{n\to\infty} I_n.
lim
n
→
∞
I
n
.
2009 Tokyo Institute of Technology, Master Course in Mathematics
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