how to integrate √[ (1+y)/(1-y) ]dy from -1 to 0

Question

integrate √[ (1+y)/(1-y) ]dy

 

from -1 to 0 

 

the answer is: (pi/2) -1

Answer 1

Make subsitution y=cos2t. Then  √[(1+y)/(1-y)]=cot(t), dy=2sin(2t).

Since -1≤y≤0, -π/4≤y≤-π/2 and 

∫_-1⁰√[ (1+y)/(1-y) ]dy=-4∫_-π/4^-π/2cos²(t) dt=/ I guess you can evaluate it/