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1
1 Further Integration
1.34
Hyperbolic area
1.36
Hyperbolic triangles
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1.35
Graph of the hyperbola
y
=
x
y=x
y
=
-
x
y=-x
\curve
(120,200,125,190)
\curve
(120,200,115,190)
\curve
(250,100,240,95)
\curve
(250,100,240,105)
y
y
x
x
\curve
(224,4, 200,30.7, 185,48.8, 180,55.3, 175,62.3, 170,70, 165,79.4,162,87.2,161,91, 160,100,161,109,162,112.8,165,120.6,170,130,175,137.7,180,144.7,185,151.2,200,169.3,224,196)
\curve
(16,4,40,30.7,55,48.8,60,55.3,65,62.3,70,70,75,79.4,78,87.2,79,91, 80,100,79,109,78,112.8,75,120.6,70,130,65,137.7,60,144.7,55,151.2,40,169.3,16,196)
\curve
(120,100,185,151.2)
\curvedashes
[2mm]1,2,1,2
\curve
(185,151.2,185,100)
P
=
(
a
cosh
v
,
a
sinh
v
)
P=(a\cosh v,a\sinh v)
Q
=
(
a
cosh
v
,
0
)
Q=(a\cosh v,0)
\curvedashes
[1mm]1,1,1,1
\curve
(20,0,220,200)
\curve
(120,100,220,0)
\curve
(20,200,110,110)
O
O
A
A