The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q. At what height above the diameter should the horizontal line be placed so as to minimize the shaded area?

Question

I would post the figure but the website is not allowing it.

I've tried using the equation for a circle and got x^2 + y^2 = 1, and used that to solve for x, x=sqrt(1-y^2), to integrate but can't seem to get the answer.

Answer 1

What is the shaded area?