Answer:
The area between the x-axis and the given curve equals 1/6 units.
Step-by-step explanation:
given any 2 functions f(x) and g(x) the area between the 2 figures is calculated as
[tex]A=\int_{x_1}^{x_2}(f(x)-g(x))dx[/tex]
The area needed is shown in the attached figure
The points of intersection of the given curve and x-axis are calculated as
[tex]x-x^2=0\\\\x(1-x)=0\\\\\therefore x=0,x=1[/tex]
hence the points of intersection are[tex](0,0),(1,0)[/tex]
The area thus equals
[tex]A=\int_{0}^{1}(x-x^2-0)dx\\\\A=\int_{0}^{1}xdx-\int_{0}^{1}x^2dx\\\\A=1/2-1/3\\\\A=1/6[/tex]
