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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

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