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Evaluate int0^(pi/4) (e^(secx) (sin(x+(p...

Evaluate `int_0^(pi/4) (e^(secx) (sin(x+(pi/4)))/(cosx(1-sinx)) dx`

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`1/2(1+sqrt2)e^(sqrt2)-(e/sqrt2)`
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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. Evaluate int0^sqrt3 (1/(1+x^2)) sin^(-1)((2x)/(1+x^2)) dx

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  2. Evaluate : int0^(pi//2) cos^3xcdot sinx dx

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  3. Evaluate int0^(pi/4) (e^(secx) (sin(x+(pi/4)))/(cosx(1-sinx)) dx

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  4. If absalt1 show that int0^pi (log(1+acosx))/cosx dx= pisin^(-1)a

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  5. If Un=int0^pi (1-cosnx)/(1-cosx) dx where n is positive integer or zer...

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  6. Prove that int0^x e^(xt)e^(-t^2)dt =e^(x^2/4) int0^xe^(-t^2/4)dt

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  7. Find a function g:R rarr R continous in [0,infty] satisfying g(0) =1 a...

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  8. Evaluate underset(nrarrinfty)lim 1/n overset(4n)underset(r=1)sum r/(sq...

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  9. If In=int0^1 x^ntan^(-1)x dx then prove that (n+1)In +(n-1)I(n-2)=(pi/...

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  10. If f(x)=x+int0^1(xy^2+x^2y) dy find f(x)

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  11. The total number of distinct x in[0,1] for which int0^x t^2/(1+t^4) dt...

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

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  13. underset(nrarrinfty)lim((n+1)(n+2)....3n)/(n^(2n)))^(1/n) is equal to

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  14. int0^5 ((1/x)-1) dx= ?

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  15. The value of underset(nrarrinfty)lim {(sqrt(n+1) +sqrt(n+2) +......+sq...

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  16. if [x] denotes the greatest integer less than or equal to x then integ...

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  17. (phi)t={1, for 0lelt1 0 otherwise then int(-3000)^(3000) (underset(r...

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

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

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

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