InterviewSolution
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InterviewSolution
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`int_(0)^(1//sqrt(2))(sin^(-1)x)/((1-x^(2))^(3//2))dx=?`A. `(1)/(2)(pi-log2)`B. `((pi)/(2)-2log2)`C. `((pi)/(4)-(1)/(2)log2)`D. none of these |
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Answer» Put `x=sint` and `dx=cost dt` `[x=0impliessint=0impliest=0]` and `[x=(1)/(sqrt(2))impliessint=(1)/(sqrt(2))impliest=(pi)/(4)]` `:. I=int_(0)^(pi//4)(tcost)/(cos^(3)t)dt=int_(0)^(pi//4)t sec^(2)t=[t tant]_(0)^(pi//4)-int_(0)^(pi//4)tant dt` `=(pi)/(4)+[logcost]_(0)^(pi//4)=(pi)/(4)+log.(1)/(sqrt(2))=((pi)/(4)-(1)/(2)log2)` |
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