Answer :

It is know that sin-1x+cos-1x = π/2




Tip – If f1(x) and f2(x) are two functions , then an integral of the form can be INTEGRATED BY PARTS as


where f1(x) and f2(x) are the first and second functions respectively.


Now, for the first term,


Taking f1(x) = sin-1√x and f2(x) = 1,






Taking (1-x)=a2,


-dx=2ada i.e. dx=-2ada


Again, x=1-a2






Replacing the value of a, we get,




The total integration yields as


, where c’ is the integrating constant


For the second term,


Taking f1(x) = cos-1√x and f2(x) = 1,






Taking (1-x)=a2,


-dx=2ada i.e. dx=-2ada


Again, x=1-a2






Replacing the value of a, we get,




The total integration yields as


, where c’’ is the integrating constant





where c is the integrating constant


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