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Evaluate: int0^(100)(x-[x]dx(w h e r e[d...

Evaluate: `int_0^(100)(x-[x]dx(w h e r e[dot]` represents the greatest integer function).

Text Solution

Verified by Experts

The correct Answer is:
`50`
`x[x]={x}` has period 1
Thus, `int_(0)^(100)(x-[x])dx=100 int_(0)^(1){x}dx`
`=100int_(0)^(1)x dx=100/2[x^(2)]_(0)^(1)=50`
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