Final answer:
To find the centroid of a constant density region bounded by the y-axis and curves, use the formula x = (integral of x * dA) / (integral of dA) and y = (integral of y * dA) / (integral of dA), where x and y are the coordinates of the centroid and dA is an infinitesimal element of area.
Step-by-step explanation:
The centroid of a constant density region bounded by the y-axis and curves can be found using the formula:
x = \frac{\int x \cdot dA}{\int dA}
y = \frac{\int y \cdot dA}{\int dA}
where x and y are the coordinates of the centroid, dA is an infinitesimal element of area, and the integrals are taken over the region. To find the centroid, we need to know the equations of the curves that bound the region and determine the limits of integration.