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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
150
150
Part of
2006 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 150
Source: Kanazawa University entrance exam 1987
9/2/2006
Find the value of
a
a
a
such that
lim
n
→
∞
3
2
∫
−
a
3
a
3
(
1
−
t
3
n
)
n
t
2
d
t
=
2
(
n
=
1
,
2
,
⋯
)
.
\lim_{n\to\infty}\frac{3}{2}\int_{-\sqrt[3]{a}}^{\sqrt[3]{a}}\left(1-\frac{t^{3}}{n}\right)^{n}t^{2}\ dt=\sqrt{2}\ \ (n=1,2,\cdots).
lim
n
→
∞
2
3
∫
−
3
a
3
a
(
1
−
n
t
3
)
n
t
2
d
t
=
2
(
n
=
1
,
2
,
⋯
)
.
calculus
integration
limit
logarithms
calculus computations