Approximation question -- How does this approximation simplify the integral?

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SUMMARY

The discussion centers on the simplification of integrals through approximation techniques, specifically by treating the integrand as a constant evaluated at the midpoint (z'=0). This method reduces the complexity of the integral significantly. The conditions l << λ and k_z << π are critical, ensuring that the exponential function's argument remains small, thereby validating the approximation's effectiveness.

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how does this aproximation reduse the integral
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Where are lambda and k_z in the integral?

The approximation simply assumes the integrand to be constant, evaluates it at the midpoint (z'=0) and multiplies it with the range z' takes.
 
so its because r'=0 ??
then why we need
l<<lambda kz<<pi
?
 
The exponential function should not change its argument too much, so kzl/r should be small compared to 1.
 

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