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Today's Calculation Of Integral
2007 Today's Calculation Of Integral
186
186
Part of
2007 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 186
Source: Tohoku University entrance exam/Science 2007
2/28/2007
For
a
>
0
,
a>0,
a
>
0
,
find
lim
a
→
∞
a
−
(
3
2
+
n
)
∫
0
a
x
n
1
+
x
d
x
(
n
=
1
,
2
,
⋯
)
.
\lim_{a\to\infty}a^{-\left(\frac{3}{2}+n\right) }\int_{0}^{a}x^{n}\sqrt{1+x}\ dx\ (n=1,\ 2,\ \cdots).
lim
a
→
∞
a
−
(
2
3
+
n
)
∫
0
a
x
n
1
+
x
d
x
(
n
=
1
,
2
,
⋯
)
.
calculus
integration
limit
calculus computations