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Techniques of Integration

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More Calculus of a Single Variable

Part of the book series: Undergraduate Texts in Mathematics ((UTM))

Abstract

By way of the Fundamental Theorem of Calculus (Theorem 10.1), many properties of integrals come from properties of derivatives and vice-versa. For example, the most basic technique of integration is to recognize the integrand as the derivative of some particular function. We saw a few examples of this sort of thing in the previous chapter. Here we focus on arguably the next two most important techniques of integration: u-Substitution which comes from the Chain Rule for derivatives, and Integration by Parts which comes from the Product Rule for derivatives.

Let us be resolute in prosecuting our ends, and mild in our methods of doing so.

—Claudio Aquaviva

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Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State, Buffalo, NY, USA

    Peter R. Mercer

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  1. Peter R. Mercer
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Mercer, P.R. (2014). Techniques of Integration. In: More Calculus of a Single Variable. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1926-0_11

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