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The value of 8/pi int0^(pi/2)((cos x)^20...

The value of `8/pi int_0^(pi/2)((cos x)^2023)/((sin x)^2023+(cos x)^2023)dx` is equal to

A

1

B

2

C

3

D

4

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The correct Answer is:
B
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Knowledge Check

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

    A
    `(pi)/(4)`
    B
    `(pi)/(2)`
    C
    0
    D
    none

  • int_(0)^(pi//2) ""(sin x - cos x)/( 1-sin x * cos x) dx is equal to

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

  • If int_(0)^(pi)((x)/(1+sinx))^(2) dx=A, then the value for int_(0)^(pi)(2x^(2). cos^(2)x//2)/((1+ sin x^(2)))dx is equal to

    A
    `A+2pi-pi^(2)`
    B
    `A-2pi+pi^(2)`
    C
    `2pi-A-pi^(2)`
    D
    None of these
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