Final answer:
To find the centroid of a region bounded by curves, calculate the coordinates x_bar and y_bar using the formulas that involve integrating the product of the coordinate and the differential area, divided by the total area.
Step-by-step explanation:
The question falls under the subject of Mathematics, specifically in the area of calculus and geometry, where the concept involved is finding the centroid (center of mass) of a planar region bounded by curves. To find the centroid, you need to calculate two coordinates: xbar and ybar. The xbar is computed using the formula:
xbar = (1/A) ∫(x dA), where A is the area of the region, x is the x-coordinate, and dA is a differential area element. Similarly, ybar is computed using the formula:
ybar = (1/A) ∫(y dA). To apply these formulas, one must first determine the area A by integrating the difference between the upper and lower curves with respect to x or y, and then evaluate the corresponding integrals for xbar and ybar. The boundaries of the integration are defined by the points where the curves intersect or by the given limits.