For example, consider the problem of finding the length of a quarter of the unit circle by numerically integrating the arc length integral. The upper half of the unit circle can be parameterized as y = 1 − x 2 . {\displaystyle y={\sqrt {1-x^{2}}}.} The interval x ∈ [ − 2 / 2 , 2 / 2 ] {\displaystyle x\in [-{\sqrt {2}}/2,{\sqrt {2}}/2]} corresponds to a quarter of the circle. Since d y / d x = − x / 1 − x 2 {\displaystyle dy/dx=-x/{\sqrt {1-x^{2}}}} and 1 + ( d y / d x ) 2 = 1 / ( 1 − x 2 ) , {\displaystyle 1+(dy/dx)^{2}=1/(1-x^{2}),} the length of a quarter of the unit circle is