Figure 5From: The curl theorem of a triangular integralTwo kinds of integrals for a monotonically increasing function.An integral along x-axis is ∫ y = f ( x ) [ A , B ] y d x = lim n → ∞ ∑ k = 1 n y k Δ x k and that along y-axis is ∫ x = f - 1 ( y ) [ A , B ] x d y = lim n → ∞ ∑ k = 1 n x k Δ y k . It holds ∫ y = f ( x ) [ A , B ] y d x + ∫ x = f - 1 ( y ) [ A , B ] x d y = x B y B - x A y A , where yA = f(xA) and yB = f(xB).Back to article page