Three semicircles of radius 1 are constructed on diameter \overline{A B} of a semicircle of radius 2 . The centers of the small semicircles divide \overline{A B} into four line segments of equal length, as shown. What is the area of the shaded region that lies within the large semicircle but outside the smaller semicircles?
Answer Choices
A. \pi-\sqrt{3}
B. \pi-\sqrt{2}
C. \dfrac{\pi+\sqrt{2}}{2}
D. \dfrac{\pi+\sqrt{3}}{2}
E. \dfrac{7}{6} \pi-\dfrac{\sqrt{3}}{2}