Lesson 4: Applying Properties of Definite Integrals Topic 6.6: Applying Properties of Definite Integrals In this section, we move beyond finite sums (rectangles) and explore what happens in the limit, as the terms become infinitely small and the number of rectangles approaches infinity. We will look at some geometric functions that may contain negative values (below the x-axis), as well as positive values (above the x-axis), and zero. Dealing With Negative Area: At times we will integrate functions that go below the x-axis (negatives). Here are a few pointers for when that happens: Area below the x-axis counts as negative area. The total area between a and b for some curve is really a net area, where the total area below the x-axis (and above the curve) is subtracted from the total area above the x-axis (and below the curve). Definite Integral Notation: Leibniz introduced the notation for the definite integral. The Greek letters of summation become Roman letters in the limit. The notation ( f(x)dx ) is read as: " The definite intergal from a tob of f of x with respect to X