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If In=int0^(pi//4) tan^n x dx , (n > 1 a...

If `I_n=int_0^(pi//4) tan^n x dx` , (`n > 1` and is an integer), then (a) `I_n+I_(n-2)=1/(n+1)` (b) `I_n+I_(n-2)=1/(n-1)` (c) `I_2+I_4,I_4+I_6, I_6+I_8` are in HP (d) `1/(2(n+1)) < I_n < 1/(2(n-1))`

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The correct Answer is:
`(1)/(2(n+1) ltI_(n) lt (1)/(2(n-1))`
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ARIHANT MATHS ENGLISH-DEFINITE INTEGRAL-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Evaluate: int(-pi//2)^(pi//2)(x^2cosx)/(1+e^x)dx

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  3. The total number for distinct x epsilon[0,1] for which int(0)^(x)(t^(2...

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

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  5. Let f'(x)=(192x^(3))/(2+sin^(4)pix) for all x epsilonR with f(1/2)=0. ...

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  6. The option(s) with the values of aa n dL that satisfy the following eq...

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  7. Let F:RtoR be a thrice differntiable function. Suppose that F(1)=0,F(3...

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  8. Let F : R to R be a thrice differentiable function . Suppose that F(...

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  9. Let f:RtoR be a function defined by f(x)={([x],xle2),(0,xgt2):} where ...

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  10. If alpha=int0^1(e^(9x+3tan^((-1)x)))((12+9x^2)/(1+x^2))dxw h e r etan^...

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  11. The integral overset(pi//2)underset(pi//4)int (2 cosecx)^(17)dx is equ...

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  12. Let f:[0,2]vecR be a function which is continuous on [0,2] and is diff...

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  13. Match the conditions/ expressions in Column I with statement in Column...

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  14. Match List I with List II and select the correct answer using codes gi...

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

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  16. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  17. The valued of int(sqrt(In2))^(sqrt(In3)) (x sinx^(2))/(sinx^(2)+sin(In...

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  18. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

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  19. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

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  20. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  21. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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