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Chapter 8: Integration

The definition of integration is quite complicated and we devote some time to studying that. We identify a class of "integrable" functions wihich is analogous to the "differentiable" functions of Chapter 4, and show that all continuous functions are integrable. Evaluating the integral based on the definition alone is very hard, so we prove the Fundamental theorem of calculus; the theoretical tool which is the basis of all the integration techniques in calculus. We then develop a more general theory of integration called Riemann-Stieltjes integration. This enables us to unify integration and summation; something which is useful in applications in mechanics and statistics, to name two.

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