Chapter 5.6, Problem 316E

In the following exercises, consider a lamina occupying the region R and having the density function p given in the preceding group of exercises. Use a computer algebra system (CAS) to answer the following questions.

a. Find the moments M and M. about the x-axis and v-ax is, respectively.

b. Calculate and plot the center of mass of the lamina.

C. [T] Use a CAS to locate the center of mass on the graph of R.

316. [T] R is the unit disk; $\rho \left(x,y\right)=3x^4+6x^2{y}^2+3y^4$