If I(n)=Int.limitsfrom 0 to pie/4 Tan^nxdx,then for any positive integer n, n(I(n-1)+I(n+1)=....

Ans:1..... Give me the complete solution

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If I(n)=Int.limitsfrom 0 to pie/4 Tan^nxdx,then for any positive integer n, n(I(n-1)+I(n+1)=.... Ans:1..... Give me the complete solution

vikas askiitian expert · Answer

K = integral (n[I n-1 + I n+1 ] ) lim 0 to pi/4 .........................1 I n+1= integral {tan n+1 xdx} lim 0 to pi/4 =integral {tan 2 xtan n-1 xdx} lim 0 to pi/4 =integral {(sec 2 x-1)tan n-1 xdx)} lim 0 to pi/4 =integral {-tan n-1 xdx + sec 2 xtan n-1 dx} I n-1 = tan n-1 xdx so I n+1 = -I n-1 + sec 2 xtan n-1 xdx lim 0 to pi/4 I n+1 + I n-1 = tan n-1 sec 2 xdx lim 0 to pi/4 ...............................2 putting 2 in 1 we get K = ntan n-1 xsec 2 xdx lim 0 to pi/4 now put tanx =t sec 2 xdx =dt K =nt n-1 dt lim 0 to 1 =t n lim 0 to 1 =1

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If I(n)=Int.limitsfrom 0 to pie/4 Tan^nxdx,then for any positive integer n, n(I(n-1)+I(n+1)=.... Ans:1..... Give me the complete solution

If I(n)=Int.limitsfrom 0 to pie/4 Tan^nxdx,then for any positive integer n, n(I(n-1)+I(n+1)=....

Ans:1..... Give me the complete solution

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