InterviewSolution
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int_0^oox^2/(1+x^6)^ndx |
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Answer» Solution :`I=int_0^oox^2/(1+x^6)^ndx` <BR> Let `x^3=tantheta` `rArr3x^2dx=sec^2thetad THETA` `x=0rArrtheta=0` ,br> `x=oorArrtheta=pi//2` `therefore I=1/3int_0^(pi/2)(sec^2thetad theta)/(sec^2theta)^N` =`1/3int_0^(pi/2)COS^(2n-2)thetad theta` =`1/3(2n-3)/(2n-2)CDOT(2n-5)/(2n-4)...1/2cdotpi/2` |
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