`int_(0)^(pi//4)sqrt(1-sin 2x)dx` का मान ज्ञात कीजिए।

Explanation

`int_(0)^(pi//4)sqrt(1-sin2x)dx`
`=int_(0)^(pi//4)sqrt(cos^(2)x+sin^(2)x-2sinx cos x)dx`
`=int_(0)^(pi//4)sqrt((cosx - sin x)^(2))dx`
`because cos x gt sinx," यदि " x in ]0,(pi)/(4)[`
`=int_(0)^(pi//4)(cos x- sinx)dx`
`=[sinx+cosx]_(0)^(pi//4)`
`=(sin.(pi)/(4)+cos.(pi)/(4))-(sin0+cos0)`
`=((1)/(sqrt2)+(1)/(sqrt2))-(0+1)=(sqrt2-1)`