MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2011 Today's Calculation Of Integral
754
754
Part of
2011 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 754
Source: 2011 Okayama University entrance exam
9/13/2011
Let
S
n
S_n
S
n
be the area of the figure enclosed by a curve
y
=
x
2
(
1
−
x
)
n
(
0
≤
x
≤
1
)
y=x^2(1-x)^n\ (0\leq x\leq 1)
y
=
x
2
(
1
−
x
)
n
(
0
≤
x
≤
1
)
and the
x
x
x
-axis. Find
lim
n
→
∞
∑
k
=
1
n
S
k
.
\lim_{n\to\infty} \sum_{k=1}^n S_k.
lim
n
→
∞
∑
k
=
1
n
S
k
.
calculus
integration
geometry
limit
calculus computations