समाकल `int_(0)^(1)sqrt((1-x)/(1+x))dx` का मान है

Options

A. `-1`
B. 1
C. `(pi)/(2)-1`
D. `(pi)/(2)+1`

Answer

C

Explanation

`I=int_(0)^(1)[sqrt((1-x)/(1+x))xx(sqrt(1-x))/(sqrt(1-x))]dx` (हर का परिमेयकारण करने पर)
`=int_(0)^(1)(1-x)/(sqrt(1-x^(2)))dx`
`=int_(0)^(1)(1)/(sqrt(1-x^(2)))dx-int_(0)^(x)(xdx)/(sqrt(1-x^(2)))`
`impliesI=[sin^(-1)x]_(0)^(1)-(1)/(2)int_(0)^(1)(2x)/(sqrt(1-x^(2)))dx`
`=[(pi)/(2)-0]+(1)/(2)[2sqrt(1-x^(2))]_(0)^(1)`
`=(pi)/(2)+[0-1]`
`=(pi)/(2)-1`