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Empirical Model Building
Published in Adedeji B. Badiru, Data Analytics, 2020
Integration by parts or partial integration is a process that finds the integral of a function that is a product of smaller functions. This is done in terms of the integral of the product of the smaller functions’ derivative and antiderivative. Many methods have evolved over the years to executing integration by parts. One method is the “DI-agonal method.” The basic form of integration by parts is presented below: ∫udv=uv−∫vdu
Concepts from Functional Analysis
Published in Karan S. Surana, J. N. Reddy, The Finite Element Method for Boundary Value Problems, 2016
Integration by parts is an important calculus tool that allows one to transfer differentiation from one function to another in an integral representation. In the following we consider line, surface and volume integrals that correspond to ℝ ≡ ℝ1, ℝ2, and ℝ3.
The impact of procedural and conceptual teaching on students' mathematical performance over time
Published in International Journal of Mathematical Education in Science and Technology, 2021
Vahid Borji, Farzad Radmehr, Vicenç Font
Implicit differentiation and integration by parts are two examples of techniques in calculus that many students tend to learn procedurally. Implicit differentiation is a technique that is used to differentiate implicit functions. Integration by parts is also a useful technique to replace a difficult integral with an integral that is easier to solve. In addition to the importance of these techniques in calculus, these two techniques are frequently used in solving differential equations. In this study, implicit differentiation and integration by parts were chosen because it seems that students even if they learn these techniques procedurally and not conceptually, might be successful in solving these types of problems. Furthermore, only a few studies have explored students’ understanding of implicit differentiation (e.g. Borji, Font, Alamolhodaei, Sánchez, & Pino-Fan, 2018) and integration by parts (e.g. Mateus, 2016) compared to other calculus concepts and procedures.
RIP: row integration by parts
Published in International Journal of Mathematical Education in Science and Technology, 2022
Integration by parts is a classic result in calculus that provides a type of product rule for finding antiderivatives or integrals of products. A goal of this paper is to convince readers that by focusing on the rows – hence the name Row Integration by Parts (RIP) – a tabular method can provide a streamlined approach for any application of integration by parts. RIP is an efficient bookkeeping tool with no loss of information. The key is that each row represents an integral and tables are to be constructed one row at a time.