Find the centroid of the region in the first quadrant bounded by the given curves.

Question

zenmo · Answer

$$y = x^3, x = y^3$$

phi · Answer

any thoughts ?

zenmo · Answer

Find the area in order to set up the integration from a to b, but no idea on how to find them algebraically by setting them equal to each other.

dominusscholae · Answer

If you the points of intersection, it will give you your bounds. Try substituting the second equation so you can find the y-intersection and then you can rule out answers given that it's in the first quadrant

phi · Answer

did you sketch the region ?

zenmo · Answer

No, my graphing skills are very bad, if I were to sketch this -- start sketching this by plotting points?

phi · Answer

yes, just a few.  for 
y= x^3
try x=0, ½, 1

zenmo · Answer

|dw:1465421916375:dw|