Chapter 5.6, Problem 313E

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.

313. [T] R is the trapezoidal region determined by the

lines $y=-\frac{1}{4}x+\frac{5}{2},y=0,$

$y=2$ and x = 0: $y=-x+3;\rho \left(x,y\right)=3xy$p(x. y) = 3xy.