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The value of int0^(pi//2) (sinx-cos x)/(...

The value of `int_0^(pi//2) (sinx-cos x)/(1+sin x cos x ) dx ` is

A

0

B

1

C

-1

D

-2

Text Solution

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The correct Answer is:
A
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int_0^(pi//2)(sinx-cos x)/(1+sinx cos x) dx

int_(0)^(pi//2) (sin x -cos x)/(1+sin x cos x) dx=?

Knowledge Check

  • int_(0)^(pi//2)(sin x - cos x)/(1-sin x cos x)dx=

    A
    1
    B
    `(pi)/(4)`
    C
    2
    D
    0

  • int_(0)^(pi//2) (sinx )/(sin x + cos x ) dx=

    A
    `pi/4`
    B
    `pi/2`
    C
    `(3pi)/4`
    D
    `(3pi)/2`

  • The value of int_(0)^(pi//2) |sin x-cos x|dx is

    A
    0
    B
    `2 (sqrt2-1)`
    C
    `2 sqrt2`
    D
    `2(sqrt2+1)`

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    int_(0)^( pi/2)(sin x-cos x)/(1+sin x*cos x)*dx

    If int_(0)^((pi)/(2))(dx)/(1+sin x+cos x)=In2, then the value of int_(0)^((pi)/(2))(sin x)/(1+sin x+cos x)dx is equal to:

    int_(0)^(pi//2) (a sin x +b cos x)/(sin x+cos x) dx =

    The value of int_(0)^(pi/2)(sin^(3)x)/(sinx+cos x) dx is

    int_(0)^(pi//2) ((cos x-sin x))/((1+sin x cos x)) dx

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