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Let f:[0,oo)vecR be a continuous strictl...

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_______

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Knowledge Check

  • 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 "_______"

    A
    `3/2`
    B
    `5/2`
    C
    `7/2`
    D
    `1/2`

  • 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

    A
    5
    B
    0
    C
    1
    D
    -5

  • Let f(x)=int_(0)^(x)f (t) dt equals

    A
    `5int_(x+5)^(5)g(t)dt`
    B
    `int_(5)^(x+5)f(t)dt`
    C
    `2int_(5)^(x+5)f(t)dt`
    D
    `int_(x+5)^(5)g(t)dt`

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