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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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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f: RvecR be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) ...

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  2. If alpha=int0^1(e^(9x+3tan^(-1)x))((12+9x^2)/(1+x^2))dx where tan^(-1)...

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  3. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

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  4. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2,pi/2) . ...

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  5. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

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  6. The option(s) with the values of aa n dL that satisfy the following eq...

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  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

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  9. Let F(x)=intx^[x^2+pi/6](2cos^2t)dt for all x in R and f:[0,1/2] -> [0...

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  10. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

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  11. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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  12. Area of the region {(x,y) in R^(2):ygesqrt(|x+3|),5ylex+9le15} is eq...

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  13. Let f:Rto(0,1) be a continuous function. Then, which of the following ...

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  14. Let f: R -> R be a differentiable function such that f(0) = 0,f(pi/2)=...

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  15. If Isum(k=1)^(98)intk^(k+1)(k+1)/(x(x+1))dx ,t h e n: (a) I<(49)/(50...

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  16. If the line x = alpha divides the area of region R = {(x,y) in R^(2) :...

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  17. If g(x)=int(sinx)^("sin"(2x))sin^(-1)(t)dt ,t h e n : (a) g^(prime)(...

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  18. For each positive integer n let y(n)=1/n((n+1)(n+2)…..(n+n)^(1//n))....

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  19. A farmer F(1) has a land in the shape of a triangle with vertices at P...

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  20. The value of the integral int(0)^(1//2)(1+sqrt(3))/(((x+1)^(2)(1-x)^(6...

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