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The value of integral int(0)^(1)sqrt((1-...

The value of integral `int_(0)^(1)sqrt((1-x)/(1+x))`dx is

A

`(pi)/(2)+1`

B

`(pi)/(2)-1`

C

`-1`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` l = int_(0)^(1) sqrt((1-x)/(1+x))`
Put `x = cos 2 theta rArr dx = -2 sin 2 theta d theta`
` :. l = int_(pi//4)^(0) sqrt((1- cos 2 theta)/(1+cos 2theta)) . 2 sin 2 theta d theta `
` = 2 int _(0)^(pi//4) (sin theta)/(cos theta) . 2 sin theta cos theta d theta`
` = 2 int_(0)^(pi//4) (1+ cos 2 theta) d theta = 2 [ theta - (sin 2 theta)/2 ] _(0)^(pi//4) = pi/2 -1 `
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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  10. The value of int (0)^(pi//2) log ("cosec "x) dx is

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  11. Which of the following is true ?

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  19. The value of int(-1)^(1) log ((x-1)/(x+1))dx is

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  21. int (1)^(2)e^(x) (1/x - 1/(x^(2)))dx is qual to

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