Synthesis of Integration Problems and Solutions

Problem synthesis is a formal task in Artificial Intelligence. This task involves the automatic generation of problems and their respective solutions across different domains (including Mathematics). Techniques for problem
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vary widely. In this paper, we present a newly designed context-free grammar (or CFG) that specifies the rules governing the formulation of specific classes of Integration problems and their solutions. These grammar rules were implemented in a software tool, and produced many Integration problems and solutions rendered in LATEX. A hundred thousand instances of these synthesised problems and solutions can be found at: tinyurl.com/integralproblems2019. The resulting problems and solution may find applications in Education (as assessment and/or practice problems), hence, aiding the learning of integration as a topic in Mathematics.