Figure 6From: The curl theorem of a triangular integralTwo kinds of integrals for a monotonically decreasing 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 ) [ B , A ] x d y = - lim n → ∞ ∑ k = 1 n x k Δ y k . It holds ∫ x = f - 1 ( y ) [ B , A ] x d y - x A ( y A - y B ) = ∫ y = f ( x ) [ A , B ] y d x - y B ( x B - x A ) , where yA = f(xA) and yB = f(xB).Back to article page