If" f, is a continuous function with `int_0^x f(t) dt->oo` as `|x|->oo`then show that every line `y = mx` intersects the curve `y^2 + int_0^x f(t) dt = 2`

Let f: RvecR be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n5) is______

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

Let f be a continuous function on [a , b]dot If F(x)=(int_a^xf(t)dt-int_x^bf(t)dt)(2x-(a+b)), then prove that there exist some c in (a , b) such that int_a^cf(t)dt-int_c^bf(t)dt=f(c)(a+b-2c)dot

If f is continuous function and F(x)=int_0^x((2t+3)dotint_t^2f(u)d u)dt , then |(F^(2))/(f(2))| is equal to_____

Let f:[0,oo)rarrR be a continuous function such that f(x)=1-2x+int_(0)^(x)e^(x-t)f(t)dt" for all "x in [0, oo). Then, which of the following statements(s) is (are)) TRUE?

Let f:R -(0,oo) be a real valued function satisfying int_0^x tf(x-t) dt =e^(2x)-1 then f(x) is

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))