About this Unit
by David Johnson

The general idea of applications of integration is to reduce the computation, the measurement, you need to do into several simpler pieces. On each little piece, the measurement can be reasonably approximated by some simplified method, and the errors in that approximation are small, getting smaller as the size of the pieces get smaller. The total measurement is the sum of the pieces, and as the size of each piece gets smaller (and the total number of pieces gets larger) the approximations go to the exact measurement in the limit. Coincidentally, the sum approaches the integral of some function over some interval. That actually describes integration itself, but it can be applied to any situation where the whole is the sum of the parts.