InterviewSolution
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int_0^1(x^5(4-x^2))/sqrt(1-x^2)dx |
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Answer» Solution :`int_0^1(x^5(4-x^2))/SQRT(1-x^2)DX` =`int_0^(pi/2)(sin^5theta(4-sin^2theta))/costheta.costhetad THETA` (where `x=sintheta` `rArr dx=costhetad theta`) =`4int_0^(pi/2)sin^5thetad theta-int_0^(pi/2)sin^7thetad theta` =`4 CDOT 4/5 cdot 2/3 - 6/7 cdot 4/5 cdot 2/3` =`8/15(4-6/7)=8/15cdot22/7=(176)/105` |
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