Integrals are often described as finding the area under a curve. This description is too narrow: it's like saying multiplication exists to find the area of rectangles. Finding area is a useful *application*, but not the purpose. Integrals help us combine numbers when multiplication can't.

This is a companion discussion topic for the original entry at http://betterexplained.com/articles/a-calculus-analogy-integrals-as-multiplication/?comply