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If l_(n)=int_(0)^(pi//4)tan^(n)xdx, n in N then l_(n+2)+l_(n) equals |
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Answer» `(1)/(N)` `rArr I_(n+2)+I_(n)=int_(0)^(pi//4)tan^(n)x(1+tan^(2)x)dx=int_(0)^(pi//4)tan^(n)x.sec^(2)xdx` `rArr I_(n+2)+I_(n)=int_(0)^(1)t^(n)DT,` where `t=tanx` `rArr I_(n+2)+I_(n)=(1)/(n+1)` |
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