`int_(0)^((pi)/(4))sin 2x dx`

Explanation

माना `I=int_(0)^(pi//4)sin 2x dx `
`=int_(0)^(pi//4)2sin x cos x dx`
माना `sin x=t" "rArr" "cos x dx = dt`
`x=(pi)/(4)" "rArr" "t=sin.(pi)/(4)=(1)/(sqrt2)`
`x= 0 " "rArr" "t=sin 0 =0 `
`therefore" "I=2int_(0)^(1//sqrt2)tdt=2[(t^(2))/(2)]_(0)^(1//sqrt2)`
`=((1)/(sqrt2))^(2)=(1)/(2)`