Chapter 13.1, Problem 55E

Density and mass Suppose a thin rectangular plate, represented by a region R in the xy-plane, has a density given by the function ρ(x, y); this function gives the area density in units such as grams per square centimeter (g/cm²). The mass of the plate is ${\displaystyle {\iint }_R\rho \left(x,y\right)dA}$. Assume that $R=\left\{\left(x,y\right):0\le x\le \pi /2,0\le y\le \pi \right\}$ and find the mass of the plates with the following density functions.

a.    ρ(x, y) = 1 + sin x

b.    ρ(x, y) = 1 + sin y

c.    ρ(x, y) = 1 + sin x sin y