The value of `int_(0)^(sqrt(2)) [ x^(2)] dx ` where `[*]` is the greatest integer function
The value of `int_(0)^(sqrt(2)) [ x^(2)] dx ` where `[*]` is the greatest integer function
A. `2-sqrt(2)`
B. `2+sqrt(2)`
C. `sqrt(2)-1`
D. `sqrt(2)-1`
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Correct Answer - C
Let `l=int_(0)^(sqrt2)[x^(2)]dx`
`int_(0)^(1)[x^(2)]dx+int_(1)^(sqrt2)[x^(2)]dx=int_(0)^(1)0dx+int_(1)^(sqrt2)1dx=(sqrt2-1)`
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