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Find the value of int(-1)^1[x^2+{x}]dx ,...

Find the value of `int_(-1)^1[x^2+{x}]dx ,w h e r e[dot]a n d{dot}` denote the greatest function and fractional parts of `x ,` respectively.

Text Solution

Verified by Experts

The correct Answer is:
`(3-sqrt(5))/2`
`int_(-1)^(1)[x^(2)+{x}]dx=int_(-1)^(0)[x^(2)+x+1]dx+int_(0)^(1)[x^(2)+x]dx`
`=0+int_(0)^((sqrt(5)-1)/2)0dx+int_((sqrt(5)-1)/2)^(1)1dx`
`=(3-sqrt(5))/2`
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