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

If `alpha=int_0^1(e^9x+3tan^((-1)x))((12+9x^2)/(1+x^2))dxw h e r etan^(-1)` takes only principal values, then the value of `((log)_e|1+alpha|-(3pi)/4)i s`

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ARIHANT MATHS-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Let F : R to R be a thrice differentiable function . Suppose that F(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Which of the following is true?

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  16. For any real number x ,l e t[x] denote the largest integer less than o...

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  17. Let f be a non-negative function defined on the interval .[0,1].If int...

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  18. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

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  19. Let Sn=sum(k=0)^n n/(n^2+k n+k^2) and Tn=sum(k=0)^(n-1)n/(n^2+k n+k...

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  20. The Integral int(pi/4)^((3pi)/4)(dx)/(1+cosx) is equal to: ...

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