Abuse notation of improper integrals

The Consortium of Asia-Pacific Education Universities

Arfi, E.^1 ; Wiryanto, L.H.^2

Study Program of Mathematic, Sumatera Institute of Technology, Lampung, Indonesia^1

Faculty of Mathematic and Natural Sciences, Bandung Institute of Technology, Ganesha Street 10, Bandung, Indonesia^2

关键词: Definite integral;    First year students;    Improper integrals;    Integration approach;    Real number;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/296/1/012056/pdf
DOI  :  10.1088/1757-899X/296/1/012056

来源: IOP

【 摘 要 】

In the definition of lbaf(x)dx, it was assumed that the interval [a, b] was finite. However, in many application in physics, engineering, economics, and probability we wish to allow a or b (or both) to be infinite or for the other case when f has an infinite discontinuity in[a, b]. In either case the integral is called mproper integral. Definition of improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or -∞ or, in some cases, as both endpoints approach limits. Many of the first-year students in ITERA learning about improper integrals make an abuse notation like written improper integral just like standard definite integral. Based on this situation, we tried to change the habits of the students in the writing of improper integrals by providing sufficient understanding and considerable exercises. It turns out this way gives good result, based on the percentage of the value of the midterms to the problem of improper integrals give a fairly good percentage value.