Page 23 - Standard Handbook Of Petroleum & Natural Gas Engineering
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12 Mathematics
In any hyperbola,
shaded area A = ab In [(x/a) + (y/b)]
In an equilateral hyperbola (a = b),
area A = a2 sinh-’ (y/a) = a2 cosh-’ (x/a)
Here x and y are coordinates of point P.
Parabola (Figure 1-14)
shaded area A = 2/3 ch
In Figure 1-15,
length of arc OP = s = 1/2 PT + 1/2 p In [cot(1/2 u)]
Here c = any chord
p = semilatus rectum
PT = tangent at P
Note: OT = OM = x
Surfaces and Volumes of Solids [I]
Regular prism (Figure 1-16)
