For the sake of ease of description let us assume that the line joining the intersection points is parallel to the
x-axis and that the whole area of intersection is in the first Cartesian quadrant.
Each of the arcs between the intersection points will be represented by a function of x, involving the square root function. The area of the intersection will be the integral of the difference of the 2 functions from the left abscissa to the right one.
There may be a way to arrive at that answer without use of calculus, but I am not familiar with it. Oh yes, there is. Draw a figure. Divide the area of intersection into 2 parts by joining the points of intersection. Draw the sectors of each of the circles involved. The area of the sector is a fraction of the area of the circle. The area of the portion of the intersection in each circle is the area of the entire sector minus the area of the triangle and the center of each circle defined by the line between the intersection points. Sorry, my description isn't too clear but once you draw the figure it will be quite clear.
