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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```
6 years ago

510 Points
```										K = integral (n[In-1  +  In+1] )      lim 0 to pi/4                .........................1
In+1= integral  {tann+1xdx}        lim 0 to pi/4
=integral {tan2xtann-1xdx}     lim 0 to pi/4
=integral {(sec2x-1)tann-1xdx)}     lim 0 to pi/4
=integral {-tann-1xdx + sec2xtann-1dx}
In-1 =  tann-1xdx so
In+1 = -In-1 + sec2xtann-1xdx           lim 0 to pi/4
In+1 + In-1 = tann-1sec2xdx             lim 0 to pi/4 ...............................2
putting 2 in 1 we get
K = ntann-1xsec2xdx          lim 0 to pi/4
now put tanx =t
sec2xdx =dt
K =ntn-1dt        lim 0 to 1
=tn        lim 0 to 1
=1
```
6 years ago
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