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“Applications of Integration” offers an intuitive development of each topic. By summing infinitely many small parts, an omega sum is obtained and then rewritten as a definite integral. Repeating this pattern several times allows readers to progress to the point of doing it themselves for calculating the work performed when pumping fluids from containers of various shapes. Topics include the finding the area between curves; determining volume using the methods of disks, washers, and shells; and calculating work with constant and variable forces, springs, and fluids. The final application is the average value of a function, which is approached directly by averaging infinitely many function values instead of the usual indirect geometric reasoning approach. |
