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

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SOLUTION :`" Let I "= int_(0)^(pi//4) sin 2 x dx`
`=int_(0)^(pi//4) 2 sin x COSX dx `
`UNDERSET(x=0 ""rArr t=sin 0=0)underset(x=(pi)/(4) ""rArr t= sin.(pi)/(4) =(1)/(SQRT(2)))("Letsin "x=t ""rArr cosx dx =dt)`
`:. I=2 int_(0)^(pi//sqrt(2))t dt = 2 [(t^(2))/(2)]_(0)^(1//sqrt(2))`
`=((1)/(sqrt(2)))^(2)=(1)/(2)`


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