An integral is the area under a curve
f(x) = y = √(1-x²)
squaring..
y² = 1 - x²
x² + y² = 1²
a bell should ring at this point. this
is the equation of a circle radius = 1 centered at 0,0. because x² is a 2-to-1 function and the limits are x=0-1, only 1/4 of the area contributes.
A = πr²/4 = π/4.
So the value of the integral is
π/4 |