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If f(x)= sum(n=1)(sin nx)/(4^(n)) and in...

If `f(x)= sum_(n=1)(sin nx)/(4^(n)) and int_(0)^(pi)f(x) dx="log" ((m)/(n))`, then the value of `(m+n)` is ….

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Knowledge Check

  • If M=int_(0)^((pi)/2)(cosx)/(x+2)dx and N=int_(0)^((pi)/4)(sinxcosx)/((x+1)^(2))dx , then the value of M-N is

    A
    `pi`
    B
    `(pi)/4`
    C
    `2/(pi-4)`
    D
    `2/(pi+4)`

  • Let f(x) = int_(0)^(pi)(sinx)^(n) dx, n in N then

    A
    `I_(n)` is rational if n is odd
    B
    `I_(n)` is irrational if n is even
    C
    `I_(n)` is an increasing sequence
    D
    `I_(n)` is a decreasing sequence

  • For every integer n, int_(n)^(n+1)f(x)dx=n^(2) , then the value of int_(0)^(5)f(x)dx=

    A
    20
    B
    25
    C
    30
    D
    35

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    If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

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