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Question
Evaluate:
`int_0^sqrt(2)[x^2]dx`
Solution
`int_0^sqrt(2)[x^2]dx`
We know greatest integer function is discontinuous when x is an integer.
∴ `int_0^sqrt(2)[x^2]dx = int_0^1 0 dx + int_1^sqrt(2) 1 dx`
= `x|_1^sqrt(2)`
= `sqrt(2) - 1`
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