Friday, 1 January 2016

integration - Simple explanation of difference between cos(x) and cos(x2) integrals.



I'm not looking for the solved integrals, I'm just looking for a simple explanation for why



cos(x2)dx



is so much more complicated than



cos(x)dx




With simple I mean something I can say to explain the difference to a person just starting to learn about integration. Perhaps something visual?


Answer



For one thing, look at their graphs. Since x increases at a constant rate, cos(x) has a constant period but x2 increases faster and faster for larger x so the "period" of cos(x2) keeps getting smaller and smaller.


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