Using a graph, it can be seen that the curves y=x+ln(x)y=x+ln⁡(x) and y=x3−xy=x3−x intersect at the points (0.447141,−0.357742)(0.447141,−0.35 7742) and (1.507397,1..507397,1.917782). find the coordinates (to three decimal places) of the centroid for the region bounded by these curves.

The area of the region bounded by two curves f(x) and g(x) is with poins of intersection at x = a and x = b is given by:



Given the curves and , the area bounded by the curves is given by:



The x-cordinate of the centroid of the area bounded by the two curves is given by:



The y-cordinate of the centroid of the area bounded by the tw.o curves is given by:



Therefore, the coordinates of the centroid of the area bounded by the given two curves is (0.985, 0.539)