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int(1/2)^(2)1/x cosec^(101)(x-1/x) dx =...

`int_(1/2)^(2)1/x cosec^(101)(x-1/x) dx =`

A

44287

B

1

C

0

D

101/2

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. int(-pi)^(pi) (sin^(4)x dx) /(sin^(4)x + cos^(x) x) =

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  2. int0^(pi) e^(cos^(2)).cos^(3) 5x dx =

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  3. int(1/2)^(2)1/x cosec^(101)(x-1/x) dx =

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  4. int(-pi/2)^(pi/2) sin^(8) x (6x^(7)-4x^(5)+3x^(3)+2x) dx =

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  5. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

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  6. int0^(1)(1-x/(1!) +x^(2)/(2!)-x^(3)/(3!) + ……oo)e^(2x) dx =

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  7. If f(x) = cos x - cos^(2)x + cos^(3)x + …. to oo int f(x) dx =

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  8. int(pi/4)^(pi/2) (cot^(4)x + cot^(2)x) dx =

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  9. If In = int0^(pi//4) tan^n x dx, then lim(n to oo) n [In + I(n -2)] eq...

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  10. If I(n) = int0^(pi/4) tan^(n)x dx, then n(I(n-1)+I(n+1)) =

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  11. If I(n) = int0^(pi/2) sin^(n)x dx then I(n)/(I(n-2)) =

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  12. int(1/sqrt3)^(x) (dx)/(1+x^(2)) = pi/6, then the upper limit x =

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  13. If int0^(k) (dx)/(2+8x^(2)) = pi/16 then k =

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  14. If int0^(k) (cos x)/(1+sin^(2)x) dx= pi/4 then k=

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  15. If int0^pi x f (sin x)dx = A int0^(pi//2) f (sin x) dx, then A is :

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  16. int(log (1/2))^(log2) sin ((e^(x)-1)/(e^(x)+1)) dx =

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  17. int0^(2pi) theta sin^2 theta cos theta d theta is equal to :

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  18. The value of integral int(-pi//4)^(pi//4) sin^(-4) x dx is :

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  19. If I(10) = int0^(pi/2) x^(10) sin x dx then I(10) + 90I(8) =

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  20. Let A = int0^(1) e^(t)/(t+1) dt, then int0^(1) (t.e^(t^(2)))/(t^(2)+1)...

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