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

If `alpha=int_0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx`
where `tan^-1x` takes only principal value, then the value of `(log_eabs(1+alpha)-(3pi)/4)` is

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. (phi)t={1, for 0lelt1 0 otherwise then int(-3000)^(3000) (underset(r...

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  2. Let f:RrarrR be a function defined by f(x)={([x],x,le,2),(0,x,gt,2):} ...

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

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

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

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  6. If f(x) + 2f(1 - x) =x^2 + 2, forall x in R, then f(x) is

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  7. The option(s) with the values of a and L that satisfy the following eq...

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

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  9. The integral int2^4 (logx^2)/((logx^2)+log(36-12x+x^2)) dx is equal to...

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  10. 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. underset(nrarrinfty)lim (sqrt1+sqrt2+.......+sqrt(n-1))/(nsqrtn) = ?

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

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

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

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  15. Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...

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

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

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

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

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  20. Given that for each a in (0,1), underset(h rarr 0)(lim) inth^(1 - h)...

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