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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


7 years ago

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										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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we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best.

Regards,
Naga Ramesh
IIT Kgp - 2005 batch

7 years ago

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