If `f(x)=1+3int_(0)^(x)t^(2)f(t)dt,` then the number of solution of `f(x)=x^(2)+1` is

If f(x)=int_(0)^(x)e^(-t)f(x-t)dt then the value of f(3) is

If f(x)=int_(1)^(x)(ln t)/(1+t)dt, then

If f(x)=int_(2)^(x)(dt)/(1+t^(4)) , then

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

Let f(x) = int_(-2)^(x)|t + 1|dt , then

Consider the function f (x) and g (x), both defined from R to R f (x) = (x ^(3))/(2 )+1 -x int _(0)^(x) g (t) dt and g (x) =x - int _(0) ^(1) f (t) dt, then The number of points of intersection of f (x) and g (x) is/are:

Let f(x)=int_(1)^(x)t(t^(2)-3t+2)dt,1lexle4 . Then the range of f (x) is

If f(x)=cos-int_(0)^(x)(x-t)f(t)dt, then f'(x)+f(x) equals

Let f(x) be a function defined by f(x)=int_(1)^(x)t(t^(2)-3t+2t)dt,1lexle3 then the maximum value of f(x) is

Let f(x) be a function defined by f(x)=int_(1)^(x)t(t^(2)-3t+2)dt,1ltxlt3 then the maximum value of f(x) is