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int_(0)^(pi/2) (sinx)/(1+cos^(2)x)dx |
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Answer» SOLUTION :`"Let " I= int_(0)^(pi//2)(sin x)/(1+COS^(2)x)dx` ` "Let" cos x=t` `rArr sin x dx =dt rArr t=cos0=1` `" and"x=(pi)/(2) rArr t=cos .(pi)/(2)=0` `:. I= int_(1)^(0)(1)/(1+t^(2))(-dt) =- int_(1)^(0)(1)/(1+t^(2))dx` `=-[TAN^(-1)t]_(1)^(0)` `=-[tan^(-1)(0)-tan^(-1)(1)]` `=-(0-(pi)/(4))=(pi)/(4)` |
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