Volumes of Regions with Known Cross Sections

Find the volume of the solid bounded by the curves y = x^2 and y = 8 - x^2 who cross sections are perpindicular to the x - axis with one side on the xy plane using semi circle cross sections

Ok so i have to find total volume which is equal to the Rheiman sum of the the volume of the semi circle which is

and where delta thickness is the change in x?

and the radius of the semi circle is 1/2 the height between y = 8 - x^2 and y = x^2

which gives

then you will have the intergral from x = -2 to x = 2 because this is where they intersect

For some reason I dont think im accurately doing this