Definite IntegrationHard
Question
If In = 
; n ∈ N, then which of the following statements hold good ?
; n ∈ N, then which of the following statements hold good ?Options
A.2nIn+1 = 2-n + (2n - 1)In
B.I2 = 
C.I2 = 
D.I2 = 
Solution
In = 
(1 + x2)-n
In = [(1 + x2)-n .x]01 + n
dx
= 2-n + 2n
dx
In = 2-n + 2n [In - In+1 ]
2n In+1 = 2-n + (2n - 1) In
Now put n = 1
2I2 = 2-1 + I1 =
+ 
dx = 
+ (tan-1 x)10
I2 =
(1 + x2)-nIn = [(1 + x2)-n .x]01 + n
dx= 2-n + 2n
dxIn = 2-n + 2n [In - In+1 ]
2n In+1 = 2-n + (2n - 1) In
Now put n = 1
2I2 = 2-1 + I1 =
+ dx = + (tan-1 x)10I2 =
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