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If I(n)=int(0)^((pi)/(4))tan^(n)thetad t...

If `I_(n)=int_(0)^((pi)/(4))tan^(n)thetad theta`, for any positive integer n, then the value of `n(I_(n-1)+I_(n+1))` is -

A

`(pi)/(2)`

B

`(pi)/(4)`

C

1

D

5

Text Solution

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The correct Answer is:
C
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 2
  1. The value of int(0)^((pi)/(2))(dx)/(1+cotx ) is -

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  2. If I(1)=int(e )^(e^(2)) (dx)/(log x) and I(2)= int(1)^(2)(e^(x))/(x)...

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  3. If I(n)=int(0)^((pi)/(4))tan^(n)thetad theta, for any positive intege...

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  4. The value of int(1)^(2)[x^(2)]dx is -

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  5. The value of int(-pi)^(pi) (2x(1+sinx))/(1+cos^(2)x)dx is equal to -

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  6. The value of int(dx)/(sinx-cosx+sqrt(2)) is -

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  7. The value of int(0)^(pi) e^(sin^(2)x) cos^(3)x dx is equal to -

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  8. Let I=int(-2)^(2)(x-[x])dx where [x] represents the greatest integer i...

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  9. The value of int(0)^(pi) (dx)/(5+3 cosx) is -

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  10. The value of int e^(x)[f(x)+f'(x)]dx is equal to -

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  11. The value of int e^(log(tan x))dx is equal to -

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  12. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

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  13. The value of int(0)^(pi) (x)/(a^(2)cos^(2)x+b^(2)sin^(2)x)dx is equal ...

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  14. If m and n are the order and degree respectively of the differential e...

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  15. If the function f(x)=(2-sqrt(x+4))/(sin2x)(x ne 0) is continuous at x ...

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  16. The integrating factor of the differential equation (x+1)(dy)/(dx)-ny=...

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  17. The solution of the differential equation (dy)/(dx)-y tan x=-2 sinx is...

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  18. The differential equation of the family of lines passing through the o...

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  19. Which of the following statements is not true ?

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  20. If f(x)={(x"sin"(1)/(x),"when "x ne 0),(0,"when "x =0):} then at x ...

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