Find the mass of the lamina that occupies the region d = {(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1} with the density function ρ(x, y) = xye^(x+y)

The mass of the lamina is 1

Step-by-step explanation:

Let be a continuous density function of a lamina in the plane region D,then the mass of the lamina is given by:

.

From the question, the given density function is .

Again, the lamina occupies a rectangular region: D={(x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}.

The mass of the lamina can be found by evaluating the double integral:

.

Since D is a rectangular region, we can apply Fubini's Theorem to get:

.

Let the inner integral be: , then

.

The inner integral is evaluated using integration by parts.

Let , the partial derivative of u wrt y is

and

, integrating wrt y, we obtain

Recall the integration by parts formula:

This implies that:

We substitute the limits of integration and evaluate to get:

This implies that:

.

Or

.

We again apply integration by parts formula to get:

.

.

.

.

No unit is given, therefore the mass of the lamina is 1.

the answer is a

step-by-step explanation:

39.00 x 24 = total installment price

carrying installment price - cash price

needed to save the .00/

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!