put x = 0 in x + sinx, you get 0
put x = pi, you get pi, which is 3.14
then x = 2pi, you get 2pi, which is 6.28
make a rough diagram
now draw a graph mirror to the blue one, which will be the inverse (red)
inverse graph can be made by taking mirror about y = x
now this inverse graph is x - sinx graph.......this we can check by sub the values like pi , 2pi etc (OR refer to method 2)
The function f(x) = x+sin(x) and its inverse f '(x) = x-sin(x) are plotted in figure.
It can be seen that inverse of f(x) is reflection about the line y=x
Let us calculate area bounded between f(x) and iis inverse between x=0 and x=π .
Hence area bounded between f(x) and iis inverse between x=0 and x= 2π is 8 sq. units
we can find the area enclosed by x + sinx and x between 0 to pi (shaded part) and multiply it with 4