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how to integrate greatest integer function
integration of [x].dx (greatest integer function) , limits from 0 to 1.5[x] ={ 0 .... 0 = x < 1{ 1 .... 1 = x < 2we have several discontinuous parts here... we actually have an improper integral...integral of [x] dx from 0 to 1.5= integral of [x] dx from 0 to 1 + integral of [x] dx from 1 to 1.5= integral of 0 dx from 0 to 1 + integral of 1 dx from 1 to 1.5= 0.5like this example in every question we break the limit in to parts like 0 to 1 ,1 to 2 ,2to 3 and so on.[x]={0, 0=<x<1 {1, 1=<x<2 {2, 2=<x<3 ............... ...............and in ths way we break the integral into parts and we integrate separate integral .Thanks & RegardsRinkoo GuptaAskIITians Faculty
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