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how to integrate greatest integer function

how to integrate greatest integer function

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1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
integration of [x].dx (greatest integer function) , limits from 0 to 1.5
[x] =
{ 0 .... 0 = x < 1
{ 1 .... 1 = x < 2

we 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

= 0.5

like 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 & Regards
Rinkoo Gupta
AskIITians Faculty

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