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"[0,oo)rarr R be a continuous and stricity increasing function such that f^(3) (x) =int_(0)^(x) tf^(2)(t) dt, x ge0 . The area enclosed by y = f(x) , the x-axis and the ordinate at x = 3 is "_______"

Let f:(0,oo)R be a continuous,strictly increasing function such that f^(3)(x)=int_(0)^(0)tf^(2)(t)dt. If a normal is drawn to the curve y=f(x) with gradient (-1)/(2), then find the intercept made by it on the y-axis is 5(b)7(c)9(d)11

Let: f:[0,3]vecR be a continuous function such that int_0^3f(x)dx=3. If I=int_0^3(xf(x)+int_0^xf(t)dt)dx , then value of I is equal to

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

Let f:R rarr R be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt. Then the value of f(1n5) is

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:(0,oo)to R be a continuous function such that F(x)=int_(0)^(x^(2)) tf(t)dt. "If "F(x^(2))=x^(4)+x^(5),"then "sum_(r=1)^(12) f(r^(2))=