Let `f:[0,oo)vecR` be a continuous strictly increasing function, such that `f^3(x)=int_0^x tdotf^2(t)dt` for every `xgeq0.` Then value of `f(6)` is_______

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

Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int_1^xf(t)dt=3xf(x)-x^3 for all xgeq1, then the value of f(2) is

Let f(x) be a continuous and differentiable function such that f(x)=int_0^xsin(t^2-t+x)dt Then prove that f^('')(x)+f(x)=cosx^2+2xsinx^2

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:[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:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . f(x) increases for

Let f:RtoR be a differentiable function such that f(x)=x^(2)+int_(0)^(x)e^(-t)f(x-t)dt . y=f(x) is

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

Find the points of minima for f(x)=int_0^x t(t-1)(t-2)dt