Mathematical proving as a way to improve understanding the concepts of integral calculus application in digital era

The aim of this study is to inform how to improve understanding concepts in the application of integral calculus in digital era through mathematical proving. The digital era is one of the characteristics of the human’s knowledge mode which is facilitated by the sophistication of information technology with the abundance of information, the overload data, but less attention to the critical power as the processor. Students quickly solve their problems with the help of technology such as calculators, computers, android and applications that support the learning that is carried out, but when asked how the process is, what concepts are used, the answer of "don’t know" and "don’t understand" frequently appear. This is because it doesn’t provide an opportunity for students to reason in strengthening their understandings of the mathematical concepts studied. The problem in this research is "How to improve the ability to understanding concepts in the application of Integral calculus in the digital era through mathematical proving?" The research method and analysis technique uses qualitative descriptive by analyzing learning theories, research results through literature review and provides few examples mathematical proofs on the volume of objects using the Application of Integral Calculus, The conclusion of this research showcases that to improve understanding of concepts in the application of integral calculus on objects volume through proof proses by setting the integration boundary of object’s base or a cross-sectional object from all possible sides.