Please explain the integration of greatest integer function in detail by taking examples of different powers of x. Don't give any link.

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Please find below the solution to the asked query:

Suppose we haveI=14x.dxNow definition of x changes at integers, henceI=01x.dx+12x.dx+23x.dx+34x.dx=010.dx+121.dx+232.dx+343.dx=0+x12+2x23+3x34=2-1+23-2+34-3=1+2+3=6 Answer

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