Final answer:
The total mass of the rectangle is approximately 810.67 m.
Step-by-step explanation:
To find the total mass of the rectangle, we need to calculate the integral of the mass density function over the given region. The mass density function is given by δ(x,y) = 2ˣ²+ʸ². We integrate this function over the region 0≤x≤2, 1≤y≤7.
Let's first integrate with respect to y, keeping x constant. The integral of y² with respect to y is (1/3)y³. Plugging in the limits of integration, we get ((1/3) * 7³) - ((1/3) * 1³) = (1/3) * 342 = 114.
Next, we integrate with respect to x, keeping y constant. The integral of 2ˣ² with respect to x is (2/3) * (2)² * x³. Substituting the limits of integration, we get ((2/3) * 4 * 2³) - ((2/3) * 4 * 0³) = (2/3) * 32 = 64/3.
Finally, we multiply the results of the two integrations together to get the total mass: (114) * (64/3) = 2432/3 = 810.67 m.