Definition of the integral for complex analysis and its mapping diagram:[br]Suppose : [math]f:\mathbb{C}\to\mathbb{C}[/math] and [math]\gamma:[a,b]\to\mathbb{C}[/math][br][b]The definite integral of[/b] [math]f[/math][br][math]\int_γf(z)dz\ =\lim_{n \to \infty}(\sum_{k=0}^{n-1}f(z_k)\Delta z_k)[/math] [br]where [math]Δz_k = z_{k+1}-z_k; z_k = γ(s_k); s_k =t_0+ kΔt; Δt=\frac{t_1-t_0}n[/math].[br]