Laplace's method

Laplace's method is a technique used in asymptotic analysis to approximate integrals of the form \[ I_n = \int_{a}^{b} e^{n f(x)} g(x) \, dx \] as \( n \) becomes large, where \( f(x) \) is a smooth function and \( g(x) \) is another function that is reasonably well-behaved.