HSC Together Year 12 Maths Advanced: Calculating Translated Definite Integrals

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# Calculating Translated Definite Integrals

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

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