Evaluate the definite integrals`int_0^ 1(dx)/(sqrt(1-x^2))`

Explanation

Let `I= int_0^1 dx/sqrt(1-x^2)`
`implies int dx/sqrt(1-x^2)=sin^(-1)x=F(x)`
by second fundamental theoem of calculus ,
`I=F(1)-F(0)`
`=sin^(-1)(1)-sin^(-1)(0)=pi/2-0=pi/2`