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Today's Calculation Of Integral
2005 Today's Calculation Of Integral
55
Today's Calculation of Integral 55
Today's Calculation of Integral 55
Source: 1993 Kyoto University
June 27, 2005
calculus
integration
limit
function
calculus computations
Problem Statement
Evaluate
lim
n
→
∞
n
∫
0
1
(
1
+
x
)
−
n
−
1
e
x
2
d
x
(
n
=
1
,
2
,
⋯
)
\lim_{n\to\infty} n\int_0^1 (1+x)^{-n-1}e^{x^2}\ dx\ \ ( n=1,2,\cdots)
n
→
∞
lim
n
∫
0
1
(
1
+
x
)
−
n
−
1
e
x
2
d
x
(
n
=
1
,
2
,
⋯
)
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