Integration of a Generalized Ratio of Polynomials

This paper provides a closed-form solution to the indefinite integral of a ratio of generalized polynomials where the denominator polynomial is raised to the general order r∈Z+. Such an integral arises in physics and engineering, the solution of which allows for closed-form analysis.

PENGEMBANGAN MOBILE LEARNING BERBASIS ANDROID DENGAN METODE KUMON UNTUK MATERI INTEGRAL TAK TENTU

This studied developed Android-based mobile learning with the Kumon method for Indefinite Integral material. This studied aims to produce a product in the form of android-based mobile learning which uses the Kumon method steps and test the level of validity and practicality to be used as a learning medium on indeterminate integral material. The research method used in this research is the Plomp method.The results of this development research was in the form of Android-based mobile learning with the Kumon method for indefinite integral material through validation test with an average presentation of 82% according to 8 validators and a practicality test with an average percentage of 67% according to 33 students SMA N 1 Bojong class XII IPA 1. From the results of this studied it can be concluded that Android-based mobile learning with the Kumon method for indefinite integral material meets the requirements with very valid and practical quality to be used as a learning medium that could be used with android in the learning process class in person or online independently on indefinite integral material.

Integrals of functions containing parameters

Calculus students are taught that an indefinite integral is defined only up to an additive constant, and as a consequence generations of students have assiduously added ‘+C’ to their calculus homework. Although ubiquitous, these constants rarely garner much attention, and typically loiter without intent around the ends of equations, feeling neglected. There is, however, useful work they can do, work which is particularly relevant in the contexts of integral tables and computer algebra systems. We begin, therefore, with a discussion of the context, before returning to coax the constants out of the shadows and assign them their tasks.

PROFESSIONAL TEACHER PROGRAM EXPERIENCE: TEACHERS’ KNOWLEDGE ON OVERCOMING STUDENTS’ MISCONCEPTION

This study aims to describe the teachers’ knowledge about students in dealing with misconceptions experienced by the student on integral material based on the experience of teachers participating in the teacher professional program (PPG). This research is qualitative research that involved two subjects who were mathematics teachers of SMA Negeri 11 Ambon. Subjects were given a chance to identify the student's misconceptions. The data is collected through observation and interviews. Based on the research results obtained information that S1 has good knowledge in diagnosing misconceptions when use three tiers test, providing treatment when the student got a different answer, and ensuring that misconceptions do not occur in student with made peer instruction in front of the class, and have a good understanding of concepts about means of constant on indefinite integral. S2 cannot diagnose misconception and S2 cannot explain the different answers when the student solves the problem using a different method. Thus, it can be stated that teachers who have the PPG experience have a better knowledge of knowing and addressing the misconceptions experienced by the student.

On sets of singular rotations for translation invariant differentiation bases formed by intervals

We study the dependence of differential properties of an indefinite integral on a rotation of the coordinate system. Namely, the following problem is studied: For a summable function f, what kind of a set may be the set of rotations θ for which {\int f} is not differentiable with respect to the θ-rotation of a given basis B? For translation invariant bases B formed by two-dimensional intervals, some classes of sets of singular rotations are found. In particular, for such bases with symmetric structure, a characterization of at most countable sets of singular rotations is found.