Re: Definite integral with huge variations in magnitude

In article <ebbips$c2t$1@xxxxxxxxxxxxxxxxxxxxxx>,
Robert Israel <israel@xxxxxxxxxxx> wrote:

There are no such wild oscillations for the function you gave us.

Aaargh! I omitted an important part, and made a typo in q. Please
accept my apologies for that. OK, here it is again:

integrand = P * Cos[600 Pi z] * (d2*Cos[k*R] - d1*Sin[k*R]) dz

where
R = Sqrt[a^2 + (q-z)^2]
P = 0.005 / (0.17708 * 8 Pi^2 R^5)
d1 = k*R * (3*a^2 - 2*R^2)
d2 = 2*R^2 + a^2 * (k^2 * R^2 - 3)

k = 400 * Pi / 3
a = 3.75E-6
q = 0.000875 (I had an extra zero in there before)

interval: z1 = -0.0025, z2 = 0.0025

Note that R, P, d1, and d2 are all functions of z.

I think you'll see it acts pretty wild between z= 0.00086 and
0.00089, having 10^11 magnitude swings.

So again, the question is what numerical integration technique would
be best for a definite integral like this?

It appears to have no analytical solution, so I have to solve it
numerically (with my own program code, not Matlab or other math
software).

-Alex
.