1. The problem statement, all variables and given/known data The figure shows a semicircle with radius 1, horizontal diameter , and tangent lines at and . At what height above the diameter should the horizontal line be placed so as to minimize the shaded area http://imgur.com/grrCqWF 2. Relevant equations The equation of a circle, x2 + y2 = a2 3. The attempt at a solution I labeled the horizontal line y=a, and chose to express the area in terms of y, with the origin at the midpoint between P and Q. So A = 0∫a √(1-y2)dy + ∫?. My problem is currently the second half of the integral as I'm evaluating the area above the function and below some other line, not above the x-axis. Should I be integrating in terms of x? Any help is appreciated, thanks.