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Let f : (0, oo) rarr R be a continuous f...

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

A

216

B

219

C

222

D

225

Text Solution

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The correct Answer is:
B
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Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

Knowledge Check

  • If f(x)= int_(0)^(x)t sin t dt , then f'(x) is

    A
    `cos x +x sin x`
    B
    `x sin x`
    C
    `x cos x`
    D
    `sin x+x cosx`

  • If f(x)= int_(0)^(x)t sin t dt , then f'(x) is

    A
    `cos x +x sin x`
    B
    `x sin x`
    C
    `x cos x`
    D
    `sin x+x cosx`

  • If f(x)=int_(0)^(x)t sin t dt , then f'(x) is

    A
    `cosx+x sin x`
    B
    `x sinx`
    C
    `x cos x`
    D
    `sinx+xcosx`

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