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If-int0^(2pi) [sinx+cosx]dx =Api and [x]...

If`-int_0^(2pi) [sinx+cosx]dx =Api` and [x] denotes the greatest integer function then A is equal to

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PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. If int0^(pi/2) sintheta log sintheta d theta =log (A/(198e)) then the ...

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  2. If int0^1 dx/((1+x)(2+x)(sqrt(x(1-x)))) = (piA)/(sqrt6(sqrt3+1)) then ...

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  3. If-int0^(2pi) [sinx+cosx]dx =Api and [x] denotes the greatest integer ...

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  4. The value of the integral sqrt2 int0^pi sqrt(1-cos2x) dx is ?

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  5. The value of the integral sqrt2 int0^(pi/2) f(sin2x) sinx dx=A (sqrt2/...

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  6. Evaluate int0^sqrt3 (1/(1+x^2)) sin^(-1)((2x)/(1+x^2)) dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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