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Find a function g:RrarrR, continuous in ...

Find a function `g:RrarrR`, continuous in `[0,oo)` and positive in `(0,oo)` satisfying `g(1)=1` and `1/2int_0^xg^2(t)dt=1/x(int_0^xg(t)dt)^2`

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The correct Answer is:
`=x^(1+sqrt2)`
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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Find a function g:RrarrR, continuous in [0,oo) and positive in (0,oo) ...

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  2. The value of int(-pi//2)^(pi//2) (x^(2)cos x )/(1+e^(x)) dx is equal ...

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

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

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  5. Let f prime(x)=(192x^3)/(2+sin^4 pix) for all x in RR with f(1/2)=0. I...

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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:R- R be a thrice differentiable function. Suppose that F(1)=0,F(...

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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: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [...

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  10. If alpha=int0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-...

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  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

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  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  13. Match the conditions/ expressions in Column I with statement in Column...

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  14. Match List I with List II and select the correct answer using codes gi...

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

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  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  17. The value of int(sqrt(ln2))^(sqrt(ln3)) (xsinx^2)/(sinx^2+sin(ln6-x^2)...

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  18. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

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  19. The value of int(0)^(1) (x^(4)(1-x)^(4))/(1+x^(2)) dx is (are)

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  20. For a in R ( the set of all real number) , a ne -1, lim(n to oo)((1^...

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  21. Consider the statements : P : There exists some x IR such that f(x)...

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