`f(x) =x^2/(1+x^3) ; g(t) = int f(t)dt`. If `g(1)=0` then `g(x)` equals-

If f(x)=e^(g(x)) and g(x)=int_(2)^(x)(dt)/(1+t^(4)) then f'(2) is equal to

Let G(x)=int e^(x)(int_(0)^(x)f(t)dt+f(x))dx where f(x) is continuous on R. If f(0)=1,G(0)=0 then G(0) equals

If f(x) = 2x^(3)-15x^(2)+24x and g(x) = int_(0)^(x)f(t) dt + int_(0)^(5-x) f(t) dt (0 lt x lt 5) . Find the number of integers for which g(x) is increasing.

f(x) : [0, 5] → R, F(x) = int_(0)^(x) x^2 g(x) , f(1) = 3 g(x) = int_(1)^(x) f(t) dt then correct choice is

f(x) : [0, 5] → R, F(x) = int_(0)^(x) x^2 g(x) , f(1) = 3 g(x) = int_(1)^(x) f(t) dt then correct choice is

If f(pi) = 2x^(3)-15x^(2)+24x and g(x) = int_(0)^(x)f(t) dt + int_(0)^(5-x) f(t) dt (0 lt x lt 5) . Find the number of integers for which g(x) is increasing.

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: