Integration in Mechanics
- A integrand with a singular point: using a limiting process or excluding a
small sphere [Jack, p.36, (1.36); p.37, l.-4-l.-1].
- Evaluate the integral given in [Jack, p.60, (2.7)].
Solution. Let x = cos g. Then dx=
-sin g dg.
Let u = 1 + (a2/y2) and v =
- (2a)/y.
ò[0, p] cos
g sin g (1 + (a2/y2)
- (2a cos g
)/y)-3 dg =
ò[-1, 1] x (u +
vx)-3 dx
= v-2 ò[u-v,
u+v]
(z - u)z-3dz
(Let z = u + vx).
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