Answer in Calculus for Yanna #205343
Find the centroid of the region bounded by the curves y= x3 and y=4x in the fourth quadrant. Sketch the bounded region.
Here the region is bounded in first and third quadrants.
So, there is no centroid at 4th quadrant.
Centroid at 1st quadrant is,
Mx = (1/2)∫ab (f(x)2 – g(x)2) dx
= (1/2)((16x3/3) – (x7/7))01
My = ∫ab x(f(x)-g(x)) dx
M = ∫ab (f(x)-g(x)) dx
= (2x2 – x4/4)“_0^1”
Thus, Centroid,(xi,yi) = (My/M,Mx/M) = (2.20408,1.48289)