MHB Find the mass and center of mass of the lamina

[carl123]

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ.
D = {(x, y) | 0 ≤ x ≤ 1, −1 ≤ y ≤ 1}; ρ(x, y) = 7xy²

I got my mass to be 7/3 but I'm not sure how to go about finding the center of mass

 

[mathmari]

The mass of the lamina is given by the formula $$m=\iint_D \rho (x, y)dA$$ and the center of mass of the lamina is $(\overline{x}, \overline{y})$ where $$\overline{x}=\frac{1}{m}\iint_D x \rho (x, y)dA \ \ \text{ and } \ \ \overline{y}=\frac{1}{m} \iint_D y \rho (x, y)dA$$

 

[carl123]

the center of mass of the lamina is $(\overline{x}, \overline{y})$ where $$\overline{x}=\frac{1}{m}\iint_D x \rho (x, y)dA \ \ \text{ and } \ \ \overline{y}=\frac{1}{m} \iint_D y \rho (x, y)dA$$

Thanks for your reply, I got (80/9 , 0) as my center of mass but it appears to be wrong, not sure why

 

[MarkFL]

Thanks for your reply, I got (80/9 , 0) as my center of mass but it appears to be wrong, not sure why

If you show your working, then perhaps it can be found where you went wrong, and how to correct it. If you simply say, "I got such and such and it is wrong, but I don't know why," this doesn't give us anything with which we can help. :)