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int(0)^(pi//4)"sin" x d(x- [x]) is equal...

`int_(0)^(pi//4)"sin" x d(x- [x])` is equal to , where [x] denotes greatest integer function-

A

`(1)/(2)`

B

`1 - (1)/(sqrt2)`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have `0 lt x lt pi//4`
`0 lt x lt 0.8`
[x] = 0
`underset(0)overset(pi//4)(int)sin x d(x-[x])`
=`underset(0)overset(pi//4)(int)sin x.d(x-0)`
=`-(cos x)_(0)^(pi//4)`
=`1 - (1)/(sqrt2)`
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