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Today's Calculation Of Integral
2010 Today's Calculation Of Integral
657
Today's calculation of Integral 657
Today's calculation of Integral 657
Source:
December 1, 2010
calculus
integration
trigonometry
limit
function
linear algebra
calculus computations
Problem Statement
A sequence
a
n
a_n
a
n
is defined by
∫
a
n
a
n
+
1
(
1
+
∣
sin
x
∣
)
d
x
=
(
n
+
1
)
2
(
n
=
1
,
2
,
⋯
)
,
a
1
=
0
\int_{a_n}^{a_{n+1}} (1+|\sin x|)dx=(n+1)^2\ (n=1,\ 2,\ \cdots),\ a_1=0
∫
a
n
a
n
+
1
(
1
+
∣
sin
x
∣
)
d
x
=
(
n
+
1
)
2
(
n
=
1
,
2
,
⋯
)
,
a
1
=
0
.Find
lim
n
→
∞
a
n
n
3
\lim_{n\to\infty} \frac{a_n}{n^3}
lim
n
→
∞
n
3
a
n
.
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