`IfI_n=int_0^1(dx)/((1+x^2)^n),w h e r en in N ,` which of the following statements hold good? (a) `2nI_(n+1)=2^(-n)+(2n-1)I_n`
(b) `I_2=pi/8+1/4` (c) `I_2=pi/8-1/4` (d) `I_3=(3pi)/(32)+1/4`

If I_n=int_0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_n

If I_n=int_0^1(dx)/((1+x^2)^n); n in N , then prove that 2nI_(n+1)=2^(-n)+(2n-1)I_n

If I_n=int_(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... then which one of the following is not true ?

Let f:(-pi/2, pi/2)->R , f(x) ={lim_(n->oo) ((tanx)^(2n)+x^2)/(sin^2x+(tanx)^(2n)) x in 0 , n in N ; 1 if x=0 which of the following holds good? (a) f(-(pi^(-))/4)=f((pi^(+))/4) (b) f(-(pi^(-))/4)=f(-(pi^(+))/4) (c) f((pi^(-))/4)=f((pi^(+))/4) (d) f(0^(+))=f(0)=f(0^(-))

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If = int_(0)^(1) x^(n)e^(-x)dx "for" n in N "then" I_(n)-nI_(n-1)=

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If I_(n)=int_(0)^(pi) e^(x)sin^(n)x " dx then " (I_(3))/(I_(1)) is equal to

If rArr I_(n)=int_(0)^(pi//4) tan ^(n)x dx , then for any positive integer, n, the value of n(I_(n+1)+I_(n-1)) is,

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