Link between Anti-Derivative and Area Under a Curve

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

In this post, we use technology or otherwise, to investigate the link between the anti-derivative and the area under a curve:

• Interpret \int_b^a f(x) dx as a sum of signed areas
• Understand the concept of the signed area function F(x) = \int_a^x f(t) dt

Definite Integrals as Area Given a Graph (Function)

Definite integrals and signed area