Online integral calculators and the concept of indefinite integral

Abstract

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This yields mismatched results of calculating the same integral on different online calculators. The paper justifies the expediency of including the interval of integration in the designation of indefinite integral or, at least, in the settings of problems of its calculation. Indication of the integration interval ensures the uniqueness of the solution to the problem of calculating the indefinite integral, the uniqueness that does not occur in the traditional setting of the integration problem. This is important because online calculators provide users with formulas that differ from each other and can represent both different and coincidental antiderivatives of the same function. Analysis of the domains of definition of the obtained by calculators antiderivatives allows users to understand how they relate to each other.