How to reduce the integral equation for light deflection?

[Bishal Banjara]

1. At pg.212, Hartle book (2003) writes equation 9.81 as an approximation of 9.80, directly. 2. $$ΔΦ=\int_0^{w_1}\frac{(1+\frac{M}{b}w)}{(1+\frac{2M}{b}w-w^2)^\frac{1}{2}}dw$$ equation(9.80)
$$ΔΦ≈\pi+4M/b$$ equation(9.81)
3. I am expecting anyone to give me a well-explained reference particularly with this method or clarify me without scaping proper steps.

 

[rude man]

Unless you can express w₁ as w₁(m,B) I don't think the definite integral can be approximated as shown.

 

[Bishal Banjara]

$$w$$ is defined as $$b/r$$. You could see the book. Otherwise, I will write a few steps back.