`intsqrt(1-cosx)dx=?`

Options

A. `-sqrt(2)"cos"(x)/(2)+C`
B. `-2sqrt(2)"cos"(x)/(2)+C`
C. `(-1)/(2)"cos"(x)/(2)+C`
D. `(-1)/(sqrt(2))"cos"(x)/(2)+C`

Answer

B

Explanation

`I=intsqrt(2sin^(2)((x)/(2)))dx=sqrt(2)intsin((x)/(2))dx`.
Put `(x)/(2)=t anddx=2dt`.
`:." "I=2sqrt(2)intsin t dt=-2sqrt(2)cos t+C`.