The graph of the function `y=f(x),` where `f : [a,b]->R` and a is a negative constant and b a positive constant, is shown.The function `F: [a,b]->R` is defined by `F(t)=int_0^t f(x) dx.` Then `F(t) > 0` for

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then f is

Let f:R to R be a function which satisfies f(x)=int_(0)^(x) f(t) dt .Then the value of f(In5), is

If A=R-{b} and B=R-{1} and function f:AtoB is defined by f(x)=(x-a)/(x-b),aneb then f is

If f(t) is a continuous function defined on [a,b] such that f(t) is an odd function, then the function phi(x)=int_(a)^(x) f(t)dt

Let f:R rarr R be a differentiable function such that its derivative f 'is continuous and f(pi)=-6. If F:[0,1]rarr R is defined by F(x)=int_(0)^(x)f(t)dt and if int(f'(x)+F(x))cos xdx=2 ,then the value of f(0) is

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=

Let f(x) be a differentiable function such that f(x)=x^2 +int_0^x e^-t f(x-t) dt then int_0^1 f(x) dx=