My (physics) book gives the following approximation:
∫π/2−π/2√1−(1−a2)sin(k)2dk≈2+(a1−b1lna2)a2+O(a2lna2)
where a1 and b1 are "(unspecified) numerical constants." I've been looking for either a derivation of this, or the same approximation listed elsewhere and have gotten nowhere. Can someone help me along?
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