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int_(0)^(pi/4) sin 2x dx |
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Answer» 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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