Oppervlakte tussen krommen: integreren met betrekking tot y

Consider a region bounded by two curves, each expressed as a function of y.

The left and the right boundary, both functions, are continuous over the interval from y=c to y=d.

These horizontal lines define the vertical extent of the region.

To find the area, the Riemann sum method is used. The region is partitioned into thin horizontal strips of equal height Δy and a base equal to the horizontal distance between the two boundary curves. The total estimated area is found by summing the areas of all thin rectangles. As Δy becomes infinitesimally small, the total area is obtained by integrating the horizontal distance with respect to y.

This method is used when the boundary curves are described in terms of y.

Consider a vapor-liquid equilibrium plot, where x and y represent the liquid- and vapor-phase mole fractions. The diagonal line, y = x, is a reference line representing equal liquid and vapor mole fractions.

The enclosed area is calculated by integrating the horizontal distance between the two curves with respect to y, providing a measure of the relative ease of separation across the full composition range.