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Let f: R rarr R be a continuous odd func...

Let `f: R rarr R` be a continuous odd function, which vanishes exactly at one point and `f(1)=1/2`. Suppose that `F(x)=int_(-1)^xf(t)dt` for all `x in [-1,2]` and `G(x)=int_(-1)^x t|f(f(t))|dt` for all `x in [-1,2]`. If `lim_(x rarr 1)(F(x))/(G(x))=1/(14)`, Then the value of `f(1/2)` is

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
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  3. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

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  7. Let F:RrarrR be a thrice differentiable function. Suppose that F(1)=0,...

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  9. Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2)...

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  11. Let f : Rrarr R be a continuous function which satisfies f(x) = int0^x...

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  12. Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2)...

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  13. Let f(x) denote the fractional part of a real number x. Then the value...

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  15. Let f : [a , b]rarr [1, infty] be a continuous function and let g : R ...

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  16. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

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  17. The following integral int(pi/4)^(pi/2) (2 cosec x)^17 dx is equal to

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  18. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

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