I was given the following problem:
Find the mass and center of mass of a lamina bounded by $y=x^4 \text{ and } y=x^2, \rho\left(x,y\right)=4$
Trying to graph these bounds gave me this image:
Assuming the lamina is in the area within the bounds - meaning the two banana-shaped areas, I would guess the center of mass is $\frac13$. But that is not the case. I will attach my work, but am I misinterpreting the picture?
Thank you!
EDIT:
It has been pointed out that my bounds of integration for y are flipped. This is true, and when corrected, the mass is the same number, just positive. The center of mass is still in the same place.
Your answer is right in magnitude but the point $A$ must lie at (0,1/3). The limits you have put on the $y$ axis must be reversed. This is because on the interval $x \in [-1,1]$, $x^4 \leq x^2$. Hope it helps!