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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 I_(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)=(pi)/(16)-(5)/(48)`

Text Solution

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The correct Answer is:
A, B
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