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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))dx` where `tan^(-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:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  2. If f(x)=x-[x], where [x] is the greatest integer less than or equal to...

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

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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. Find x+y+z

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

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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(In2)^(In3) (x sinx)dx is

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  11. Let f:[1,oo] be a differentiable function such that f(1)=2. If 6int1...

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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 epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^...

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  14. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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  15. Which of the following is true?

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  16. f(x)={(x-[x]",",if[x] "is odd"),(1+[x]-x",",if[x]" is even"):} Then,...

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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. Let I(n)=int(-pi)^(pi)(sin x)/((1+pi^(x))sin x )dx, n=0,1,2,... The va...

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  19. Let S(n)=sum(k=1)^(n)n/(n^(2)+kn+k^(2)) and T(n)=sum(k=0)^(n-1)n/(n^(2...

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  20. Then integral int(pi//4)^((3pi)/4) (dx)/(1+cosx) is equal to

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