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In = int0^(pi/4) tan^n x dx , then the v...

`I_n = int_0^(pi/4) tan^n` x dx , then the value of `n(l_(n-1) + I_(n+1))` is

A

1

B

2

C

`pi//4`

D

`pi`

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Knowledge Check

  • If I_n = int_0^(pi//4) tan^n xdx , then

    A
    `I_(10) + I_8 = 1/9`
    B
    `I_5 + I_7 = 1/6`
    C
    `I_12 + 2I_10 + I_8 = 20/99`
    D
    `I_6 - I_12 = 2/99`

  • IF I_n=int_0^(pi//4) tan^n x dx then what is I_n+I_(n+2) equal to

    A
    A. `1/n`
    B
    B. `1/((n+1))`
    C
    C. `n/((n-1))`
    D
    D. `1/((n-2))`

  • If I_(n)=int_(0)^(pi//4) tan^(n) x dx, lim_(n to oo) n(I_(n+1)+I_(n-1)) equals

    A
    1
    B
    2
    C
    `pi//4`
    D
    `pi`

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