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