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Evaluate int(-5)^(5)x^(2)[x+1/2]dx (wher...

Evaluate `int_(-5)^(5)x^(2)[x+1/2]dx` (where [.] denotes the greatest integer function).

Text Solution

Verified by Experts

The correct Answer is:
`10(e-1)`
`int_(0)^(10)e^(2x-{2x})d(x-[x])`
`=int_(0)^(10)e^([2x])dx`
`=20 int_(0)^(1//2)e^({2x})dx` ( `{2x}` has period `1//2`)
`=20 int_(0)^(1//2) e^(2x)dx`, [for `x epsilon(0,1//2),{2x}=2x`]
`=10(e^(2x))_(0)^(1//2)`
`=10(e-1)`
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