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Today's Calculation Of Integral
2011 Today's Calculation Of Integral
702
702
Part of
2011 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 702
Source: 1979 Nagoya University entrance exam/Science
6/3/2011
f
(
x
)
f(x)
f
(
x
)
is a continuous function defined in
x
>
0
x>0
x
>
0
. For all
a
,
b
(
a
>
0
,
b
>
0
)
a,\ b\ (a>0,\ b>0)
a
,
b
(
a
>
0
,
b
>
0
)
, if
∫
a
b
f
(
x
)
d
x
\int_a^b f(x)\ dx
∫
a
b
f
(
x
)
d
x
is determined by only
b
a
\frac{b}{a}
a
b
, then prove that
f
(
x
)
=
c
x
(
c
:
c
o
n
s
t
a
n
t
)
.
f(x)=\frac{c}{x}\ (c: constant).
f
(
x
)
=
x
c
(
c
:
co
n
s
t
an
t
)
.
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integration
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