2. Let r > 0, and let R be the semicircular region bounded below by the x axis and above by the circle x2 + y? = r2, that is, x² + y? = r2 with y > 0. (a) Find the center of gravity (7, g) of R. (b) Find the radius r for which (7, g) (0, T). (c) Suppose S is the quarter circular region in the first quadrant, bounded by the x axis, the axis, and the quarter circle x2 + y² = r². Without evaluating any integrals or making further computations, use symmetry considerations and computations in (a) to determine (T, 9).

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