Evaluate the following integrals:
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.
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