Using integration, find the area of the region bounded by the curve \( y = x|x| \), the x-axis, and the vertical lines \( x = -2 \) and \( x = 2 \).
Show Hint
Since \( y = x|x| \) is an odd function, the geometric shapes on either side of the origin are completely identical in area. You can find the area for the positive half and multiply it by 2.