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IfIn=int0^1(dx)/((1+x^2)^n),w h e r en i...

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

A

`2n 1 _( n+1) =2 ^(-n) + (2n -1) 1 _(n)`

B

`1 _(2) =pi/8 + 1/4`

C

` 1_(2) = pi/8 -1/4`

D

`1_(3) = (pi)/(16) - (5)/(48)`

Text Solution

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The correct Answer is:
A, B
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