Match the Column I with Column II

Answer

`AtoS;BtoS;CtoP;DtoR`

Explanation

(A) Let `I=int_(-1)^(1)(dx)/(1+x^(2))`
Put `x=tanthetarArrdx = sec^(2)thetad theta`
`:. I=2 int_(0)^(pi//4)d theta=(pi)/(2)`
(B) Let `I=int _(0)^(1)(dx)/(sqrt(1-x^(2)))`
Put ` x=sintheta`
` rArr dx = cos theta d theta`
` I = int _(0)^(pi//2) 1 d theta = (pi)/(2)`
( C) `int_(2)^(3)(dx)/(1-x^(2))=(1)/(2)[log((1+x)/(1-x))]_(2)^(3)=(1)/(2)[log((4)/(-2))-log((3)/(-1))=(1)/(2)[log((2)/(3))]`
(D) `int_(1)^(2)(dx)/(xsqrt(x^(2)-1))=[sec^(-1)x]_(1)^(2)=(pi)/(3)-0=(pi)/(3)`