In the second case, its not clear if you ask the area \ (S_1 \) of the figure formed by the union o

Elisa get from the following question:
In the first case, with reference to the figure, I think it should be understood that it requires the calculation of the area \ (S \) of the triangle dtdc tracking mixtilineal \ (ABC \), equivalent to the integral defined between \ (2- \ sqrt { 3} \) and \ (1 \) of the difference between the functions \ (y = -x ^ 2 + 4x \) and \ (y = 1 \), ie:
In the second case, its not clear if you ask the area \ (S_1 \) of the figure formed by the union of the parabolic segment bounded by the arc \ (AB \) and the triangle \ (AEB \), or rather the ' area \ (S_2 \) of the figure formed by the difference between the parabolic segment bounded by the arc \ (CD \) and the triangle \ (CED \). After identifying the various points of intersection, we calculate both relying in part to the integration and in part to simple geometric considerations, taking into account that, in the second case, to have the area in the absolute sense, that is expressed by a positive number, is must imagine to translate the whole figure of \ (5 \) drive in the direction \ (y \):
I get by Roberto request for aid in the calculation of the centers of gravity of two flat regions: 1) Determine the centroid of the region bounded by flat graphics \ (y = (x-1) ^ 2 \) and \ (y = - (x- 1) ^ 2 \) from the axis \ (y \) and the straight line \ (x = 3 \). 2) Determine the coordinates dtdc tracking of the center of gravity of the region of the first quadrant bounded by the network \ (y = 3x \), \ (y = x / 3 \) and from the graph of \ (y = 1 / x \).