Find the area of the region enclosed by the x-axis and the curve y=x*sin(x) on the interval[0,pi]. Then find the vertical line x=a that divides the region in half.

So if I take the integral of the function between 0 and pi I get the area enclosed by the x-axis and the curve of y=x*sin(x), right? If this is right, then the vertical line that divides the region in half would be the x value that is 1/2 the value of the integral?

Is this right, or am I doing it all wrong?

Thank you