A large semicircle has radius 4 and its diameter lies on the x-axis. A smaller semicircle of radius 2 has its diameter on the same axis with center at (1,0), creating a hole in the larger region. What is the exact area of the shaded region consisting of the large semicircle minus the smaller one?
a) 10π
b) 6π
c) 8π
d) 4π