Using Geometric Ideas to find the Definite Integral

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 geometric ideas to find the definite integral \int_b^a f(x) where f(x) is positive throughout an interval a≤x≤b and the shape of f(x) allows such calculations, for example when f(x) is a straight line in the interval or f(x) is a semicircle in the interval.

Evaluating Definite Integrals Using Geometry

Evaluate a Definite Integral Using a Geometric Formula (Semicircle)