Calculus 1B: Integration

18.01.2x Calculus 1B: Integration is the second of the three MITx calculus modules, sitting between Calculus 1A: Differentiation and Calculus 1C: Coordinate Systems and Infinite Series. It is organised around the integral: interpreting it geometrically as the area under a curve, discovering its connection to the derivative, and building a toolkit of techniques for integrating by hand while recognising the functions that need a computer. The syllabus starts by modelling the integral through differentials, antiderivatives, differential equations and separation of variables, moves to the theory of integration with the mean value theorem, the definition of the integral and the first and second fundamental theorems, and then to applications such as areas and volumes, average value and more.

MIT frames the material with questions about spoon handles in fondue, shapes with finite volume but infinite surface area, and zip line trajectories, and notes applications to centres of mass, beam stress, motor power and rocket distance. The course is instructor-paced, estimated at 15 weeks with 5 to 10 hours per week. Auditing is free with access to the course and materials, and the $100 certificate track adds graded assignments and exams and an MIT certificate of completion.