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`        If  I 1 =∫ sin -1 x dx    and I 2 = ∫ sin -1 √1-x 2  dx  then show that I 1 +I 2 = pie x / 2`
8 years ago

Ramesh V
70 Points
```										we shld know that
arc.sin x +arc.sin y = arc.sin ( x.(1-y2)1/2 + y.(1-x2)1/2 )  for -1 < x,y < 1and x2+y2<=1
here put y = (1-x2)1/2  and it satisfies that for -1 < x < 1 , 0< (1-x2)1/2 < 1
and  x2+1-x2=1
so I1 + I2 = integral ( arc.sin ( x2 + (1-x2)1/2.(1-x2)1/2 ))
= integral ( arc.sin ( 1 ))
= integral ( Pi/2 )
= x.Pi/2
--
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Regards,
Naga Ramesh
IIT Kgp - 2005 batch
```
8 years ago
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