Approximation of the Area using Shapes

This is part of the HSC Mathematics Advanced course under the topic of Integral Calculus: Areas and the definite integral

In this post, we determine the approximate area under a curve using a variety of shapes including squares, rectangles (inner and outer rectangles), triangles or trapezia and consider functions which cannot be integrated into the scope of this syllabus and explore the effect of increasing the number of shapes used.

Area under Curves (3 of 4: Where do the components of Riemann’s integral come from?)

Area under Curves (4 of 4: Testing Riemann’s Integral for areas under simpler relationships)

Approximating a Definite Integral Using Rectangles

Area under Curves (Continued) (1 of 2: Relationship between Differentiation and Integration)

Area under Curves (Continued) (2 of 2: Why definite integrals do not take into account the constant)