**ERIC Number:**EJ838167

**Record Type:**Journal

**Publication Date:**2005-Dec

**Pages:**4

**Abstractor:**As Provided

**Reference Count:**1

**ISBN:**N/A

**ISSN:**ISSN-1051-1970

Using Linear Algebra to Do an Integration by Parts Example

Sprows, David J.

PRIMUS, v15 n4 p303-306 Dec 2005

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that "[integral](au + bv)dx = a [integral] udx + b [integral] vdx", and the inverse relationship between the integral and the derivative. This approach has the advantage of being more direct than the standard one. Moreover, it can be generalized to apply to a wide range of similar integrals using the tools of linear algebra.

Descriptors: Algebra, Mathematics Instruction, Equations (Mathematics), Matrices, Mathematical Formulas, Problem Solving, Teaching Methods, College Mathematics

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A