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Evaluate: int(-5)^5x^2[x+1/2]dx(w h e r ...

Evaluate: `int_(-5)^5x^2[x+1/2]dx(w h e r e[dot]` denotes the greatest integer function).

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Verified by Experts

Let `I=int_(-5)^(5)x^(2)[x+1/2]dx`
`=int_(-5)^(5)x^(2)(-x+1/2]dx` (Replacing `x` by `-x`)
`=int_(-5)^(5)x^(2)[-x-1/2+1]dx`
`=int_(-5)^(5)([-x-1/2]+1)dx`
`=-int_(5)^(5)x^(2)[x+1/2]dx`
`=-I`
`:.I=0`
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