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Evaluate int(-1)^(1){x}dx, {x} is fracti...

Evaluate `int_(-1)^(1){x}dx`, `{x}` is fractional part function.

Text Solution

Verified by Experts

Let `I=int_(-1)^(1){x}dx=int_(-1)^(1)(x-[x])dx=int_(-1)^(1)xdx-int_(-1)^(1)[x]dx`
`=(1)/(2)[x^(2)]_(-1)^(1)-{int_9-1)^(0)[x]dx+int_(0)^(1)[x]dx+int_(0)^(1)[x]dx}=0-{int_(-1)^(0)-1dx+int_(0)^(1)0dx}=int_(-1)^(0)dx=1`
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