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