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The valueof the integral `int_0^(1/2)(1+sqrt(3))/(((x+1)^2(1-x)^6)^(1/4))dx`is ______. |
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Answer» Correct Answer - 2 `I=int_(0)^(1//2)(1+sqrt(3))/(((x+1)^(2)(1-x)^(6))^(1//4))dx` `=int_(0)^(1//2) ((1+sqrt(3))dx)/((1+x)^(2)[((1-x)^(6))/((1+x)^(6))]^(1//4)` Put `(1-x)/(1+x)=t` `implies(-2dx)/((1+x)^(2))=dt` `:.I=int_(1)^(1//3)((1+sqrt(3))dt)/(-2t^(3//2))=(-(1+sqrt(3)))/2xx|(-2)/(sqrt(t))|_(1)^(1//3)` `=(1+sqrt(3))(sqrt(3)-1)=2` |
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