Evaluate the double integral ∬ x - 3y² da, where R= = 0 ≤x ≤ 6, 2≤ y≤4

Question

Evaluate the double integral ∬ x - 3y² da, where R= = (x, y)

Answer 1

To evaluate the double integral ∬ x - 3y² da, we need to express the limits of integration in terms of x and y and set up the integral using the appropriate differential elements. Finally, we solve the integral to find the numerical value.

Step-by-step explanation:

To evaluate the double integral ∬ x - 3y² da, first, we need to express the limits of integration in terms of x and y. In this case, the region R is defined as (x, y) . Next, we express the integrand, x - 3y², in terms of x and y.

Then, we set up the double integral by integrating the expression x - 3y² with respect to da, where da represents the infinitesimal area element. We use the limits of integration and the appropriate differential elements to calculate the double integral.

Finally, we solve the double integral to find the numerical value of the integral over the region R.