Final answer:
To find the mass of the region bounded by x and y with the density function x,y=3*x*y, we need to integrate the density function over the given region. In this case, the region is not provided, so we cannot calculate the mass accurately.
Step-by-step explanation:
To find the mass of the region bounded by x and y with the density function x,y=3*x*y, we need to integrate the density function over the given region. In this case, the region is not provided, so we cannot calculate the mass accurately. However, if we assume a square region with side length 1, the mass would be:
Mass = ∫∫(3xy) dA
Integrating the function with respect to x and y over the region [0,1]x[0,1], we get:
Mass = 3∫∫(xy) dA = 3 ∫(0 to 1) ∫(0 to 1) (xy) dx dy
To evaluate this integral, we integrate first with respect to x and then with respect to y:
Mass = 3 ∫(0 to 1) [(x^2)y/2] (from x= 0 to 1) dy = 3 ∫(0 to 1) (y/2) dy
Simplifying further, we get:
Mass = 3 [y^2/4] (from y=0 to 1) = 3/4 = 0.75 units of mass