InterviewSolution
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InterviewSolution
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Evaluate : `(i) int_(0)^(1//2)(dx)/(sqrt(1-x))` `(ii) int_(0)^(1)((1-x)/(1+x))dx` |
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Answer» `(i) int_(0)^(1//2)(dx)/(sqrt(1-x))=int_(0)^(1//2)(1-x)^(-1//2)dx=[(2sqrt(1-x))/(-1)]_(0)^(1//2)=(2-sqrt(2))`. `(ii) int_(0)^(1)((1-x)/(1+x))dx=int_(0)^(1)(-1+(2)/(x+1))dx` [on dividing `(-x+1)` by `(x+1)`] `=[-x+2log|x+1|]_(0)^(1)=[(2log2)-1]`. |
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