what is integration of 1/(a^2-2*a*cos(x)+1) its lower limit is 0 and upper limit is pie

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vikas askiitian expert · Answer

I= dx/[a 2 -2acosx +1] lim 0 to pi put cosx = 1-tan 2 x/2/1+tan 2 x/2 I= sec 2 x/2 dx / [(a-1) 2 + (a+1) 2 tan 2 x/2] now put tanx/2 = t sec 2 x/2dx =2dt I = 2dt / [(a-1) 2 +(a+1) 2 t 2 ) I =2dt/(1+a) 2 .[(a-1/a+1) 2 + t 2 ] this integral is same as 1/a 2 +x 2 dx & its integral is tan -1 (x/a)/a so I =2/(a 2 -1)tan -1 [(a+1)t/(a-1)] I = 2/(a 2 -1)tan -1 [(a+1)tanx/2/(a-1)] lim 0 tp pi taking limit I =2/(a 2 -1) [ tan -1 infinity -tan -1 0] =pi/(a 2 -1) ans

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what is integration of 1/(a^2-2acos(x)+1) its lower limit is 0 and upper limit is pie

what is integration of 1/(a^2-2acos(x)+1) its lower limit is 0 and upper limit is pie

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