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What is int(0)^(sqrt(2))[x^(2)] dxequal ...

What is `int_(0)^(sqrt(2))[x^(2)] dx`equal to (where `[.]` is the greatest integer function ) ?

A

`sqrt(2) - 1`

B

`1-sqrt(2)`

C

`2(sqrt(2) - 1)`

D

`sqrt(3) - 1`

Text Solution

Verified by Experts

The correct Answer is:
A
`int_(0)^(sqrt(2))[x^(2)] dx`
`= int_(0)^(1) [x^(2)] dx + int_(1)^(sqrt(2)) [x^(2)] dx`
`= 0+int_(1)^(sqrt(2)) 1.dx` ( `:' []` is greaest integer function)
`(x)_(1)^(sqrt(2)) = (sqrt(2)) - 1`.
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