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If F(x) = int(x+sinx)/(1+cosx)dx and F(0...

If `F(x) = int(x+sinx)/(1+cosx)dx` and `F(0)=0`then the value of `F(pi/2)` is

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Knowledge Check

  • If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

    A
    `1/(3+e)`
    B
    `(5-e)/(3-e)`
    C
    `(2+e)/(e-2)`
    D
    none of these

  • If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

    A
    `e((pi)/(4)-(1)/(2))+1`
    B
    `e((pi)/(4)+(1)/(2))+1`
    C
    `e((pi)/(2)-(1)/(4))+1`
    D
    `e^(-1)((pi)/(4)-(1)/(2))+1`

  • If int_(0)^(npi) f(cos^(2)x)dx=k int_(0)^(pi) f(cos^(2)x)dx , then the value of k, is

    A
    1
    B
    n
    C
    `n//2`
    D
    none of these

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    The function f(x)=(1-sinx+cosx)/(1+sinx+cosx) is not defined at x=pi . The value of f(pi) so that f(x) is continuous at x=pi is

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