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Today's Calculation Of Integral
2011 Today's Calculation Of Integral
726
726
Part of
2011 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 726
Source: 1976 Aoyama Gakuin University entrance exam
6/27/2011
Let
P
(
x
,
y
)
(
x
>
0
,
y
>
0
)
P(x,\ y)\ (x>0,\ y>0)
P
(
x
,
y
)
(
x
>
0
,
y
>
0
)
be a point on the curve
C
:
x
2
−
y
2
=
1
C: x^2-y^2=1
C
:
x
2
−
y
2
=
1
. If
x
=
e
u
+
e
−
u
2
(
u
≥
0
)
x=\frac{e^u+e^{-u}}{2}\ (u\geq 0)
x
=
2
e
u
+
e
−
u
(
u
≥
0
)
, then find the area bounded by the line
O
P
OP
OP
, the
x
x
x
axis and the curve
C
C
C
in terms of
u
u
u
.
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