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Let f(x) = tan^(-1) ((1+cos x)/(sinx)) a...

Let `f(x) = tan^(-1) ((1+cos x)/(sinx)) and g (x) = tan^(-1) ((sinx)/(1-cos x))`
` int f(x) dx = `

A

`(pix)/2 - x^(2)/4 + c`

B

` pix - (x^(2))/4 + c`

C

` pi x + (x^(2))/4 + c`

D

none of these

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Let f(x) = tan^(-1) ((1+cos x)/(sinx)) and g (x) = tan^(-1) ((sinx)/(1-cos x)) int {f(x)+g(x)}dx =

    A
    `(pix)/2 - (x^(2))/4 + c`
    B
    `pix - (x^(2))/2 + c`
    C
    ` (pix)/2 + (x^(2))/4+c`
    D
    `pix+(x^(2))/2 + c`

  • Let f(x) = tan^(-1) ((1+cos x)/(sinx)) and g (x) = tan^(-1) ((sinx)/(1-cos x)) int {f(x) - g (x)}dx =

    A
    `pix+c`
    B
    `(x^(2))/2+c`
    C
    0
    D
    `pix+x^(2)+c`

  • Let f(x) = int_(-1)^x abs(x+1) dx then

    A
    f(x) is continous in (-1,1)
    B
    f(x) is differentiable in (-1,1)
    C
    f'(x) is continous in (-1,1)
    D
    All of the above

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