If `f(x)=min{|x-1|,|x|,|x+1|` and `I=int_(-1)^(1)f(x)dx` then value of

If f(x)=min{|x-1|,|x|,|x+1|, then the value of int_-1^1 f(x)dx is equal to

If f(x) =(e^x)/(1+e^x), I_1=int_(f(-a))^(f(a)) xg(x(1-x))dx , and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx, then the value of (I_2)/(I_1) is

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

Suppose f, f' and f'' are continuous on [0, e] and that f'(e )= f(e ) = f(1) = 1 and int_(1)^(e )(f(x))/(x^(2))dx=(1)/(2) , then the value of int_(1)^(e ) f''(x)ln xdx equals :

If f(x)=(e^x)/(1+e^x), I_1=int_(f(-a))^(f(a))xg(x(1-x)dx and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx , then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1

If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int_(-1)^1f(x)dxdot

If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int_(-1)^1f(x)dxdot

If f'(x)=f(x)+ int_(0)^(1)f(x)dx , given f(0)=1 , then the value of f(log_(e)2) is

If f is continuous on [0,1] such that f(x)+f(x+1/2)=1 and int_0^1f(x)dx=k , then value of 2k is 0 (2) 1 (3) 2 (4) 3

If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), then find the value of int_(-3)^5g(x)dx .