HP HP-15C - Page 61

Section 2: Working With (7T) 59
1.000401708155 ± 1.2 X 10~12.
A final example drawn from real life involves the electrostatic field
about an ellipsoidal probe with principal semiaxes a, b, and c:
dx
(a2 + x)V(a2 + x)(b2 + x)(c2 + x)
for a = 100, 6 = 2, and c = 1.*
Transform this improper integral to a proper one by substituting
V=p
rl
J r
where
p = 2/((a2 - c2)^ a2 - b2 ) = 2.00060018 X 10~6
q = (b2- c2)/( a2 - b2) = 3.001200480 X 10'3
r=c/a = 0.01 .
However, this integral is nearly improper because q and r are both
so nearly zero. But by using an integral in closed form that
sufficiently resembles the troublesome part of V, the difficulty can
be avoided. Try
fl
= p\
_
du/\/u2 + q = p \n(u + -J u2 + q )
Then
= 8.40181880708 X 10"6.
/w
J r
V=W
u'2 + q)du
=}du.
*From Stratton, J.A., Electromagnetic Theory, McGraw-Hill, New York, 1941,
pp. 201-217.