" If "X=int_(0)^(oo)(dt)/((1+t^(2))(1+t^(2017)))," then "(3x)/(pi)" is equal to "

If int_(0)^(x)f(t)dt=x^2+int_(x)^(1)t^2f(t)dt , then f((1)/(2)) is equal to

If int_(0)^(x)f(t)dt=x^(2)+int_(x)^(1)t^(2)f(t)dt, then f'((1)/(2)) is

If int_(1)^(x) (dt)/(|t|sqrt(t^(2)-t)) = (pi)/(6) , then x can be equal to :

If f(x)=x+int_(0)^(1)t(x+t)f(t)dt, then the value of (23)/(2)f(0) is equal to

The value of int_(1//e)^(tanx)(t)/(1+t^(2))dt+int_(1//e)^(cotx)(1)/(t(1+t^(2)))dt , where x in (pi//6, pi//3 ), is equal to :

The value of int_((1)/(epsilon))^(tan x)(tdt)/(1+t^(2))+int_((1)/(epsilon))^(cot x)(dt)/(t(1+t^(2))), where x in((pi)/(6),(pi)/(3)), is equal to: (a)0(b) 2 (c) 1 (d) none of these

If f(x)=int_(0)^(x)(sin^(4)t+cos^(4)t)dt, then f(x+pi) will be equal to

If int_(1)^(x)(dt)/(|t|sqrt(t^(2)-1))=(pi)/(6) then x can be equal to

If int_(0)^(1) f(t)dt=x^2+int_(0)^(1) t^2f(t)dt , then f'(1/2)is