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 the formula \int_b^a f(x) dx = F(b) - F(a) , where F(x) is the anti-derivative of f(x) , to calculate definite integrals:
- Understand and use the Fundamental Theorem of Calculus, F′(x) = \frac{d}{dx} [ \int_a^x f(t) dt] = f(x) and illustrate its proof geometrically
- Use symmetry properties of even and odd functions to simplify calculations of area
- Recognise and use the additivity and linearity of definite integrals
- Calculate total change by integrating the instantaneous rate of change
Khan Academy Fundamental theorem of calculus (Part 1)
