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The video tutorial discusses finding the centroid of a shaded area by locating the centroid x bar and y bar. The area is divided into four parts - one shaded and three non-shaded. For a quarter circle with radius 3, the area is pi/4*r^2 and the centroid formula is 4r/3pi for x bar and y bar. Simplifying the formula for x bar and y bar where r=3 gives 4/pi. Finally, the x a and y a components are calculated by multiplying x bar and y bar by the area, resulting in x a=9 and y a=9.
