निम्नलिखित समाकलों के मान ज्ञात कीजिए-
`int_(0)^(pi//2) sqrt(1-cos 2x) dx`

Explanation

`underset(0)overset(pi//2)int sqrt(1-cos 2x)dx`
`underset(0)overset(pi//2)int sqrt(2sin^(2))dx`
`underset(0)overset(pi//2)int sqrt(2) |sin x|dx`
`2underset(0)overset(pi//2)int sin xdx` `[therefore sin x ge 0 "जबकि "0 lt x lt pi/2]`
`=sqrt2[-cos]_(0)^(pi//2)`
`=sqrt2[(-cos""pi/2)-(-cos 0)]`
`=sqrt2[0+1]=sqrt2`