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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
152
152
Part of
2006 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 152
Source: Fukui University entrance exam/Engineering 1970
9/6/2006
Let
f
(
x
)
f(x)
f
(
x
)
the function such that
f
(
0
)
=
0
,
∣
f
′
(
x
)
∣
≤
1
1
+
x
(
x
≥
0
)
.
f(0)=0,\ |f'(x)|\leq \frac{1}{1+x}\ (x\geq 0).
f
(
0
)
=
0
,
∣
f
′
(
x
)
∣
≤
1
+
x
1
(
x
≥
0
)
.
Prove that
∫
0
e
−
1
{
f
(
x
)
}
2
d
x
≤
e
−
2.
\int_{0}^{e-1}\{f(x)\}^{2}dx\leq e-2.
∫
0
e
−
1
{
f
(
x
)
}
2
d
x
≤
e
−
2.
calculus
integration
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calculus computations