`intsqrt(1+sinx)dx`

Options

A. `-sqrt(2)sin((pi)/(4)-(x)/(2))+C`
B. `sqrt(2)sin((pi)/(4)-(x)/(2))+C`
C. `-2sqrt(2)sin((pi)/(4)-(x)/(2))+C`
D. none of these

Answer

C

Explanation

`(1+sinx)=1+cos((pi)/(2)-x)=2cos^(2)((pi)/(4)-(x)/(2))`.
`:." "I=sqrt(2)intcos((pi)/(4)-(x)/(2))dx." Put "((pi)/(4)-(x)/(2))=t and (-1)/(2)dx=dt`.
`I=-2sqrt(2)cost" dt"=-2sqrt(2)sint+C`.