Question

Use a double integral to find the area of the region D in a given scenario.

a) Count the number of rectangles in D
b) Add the values of D's boundaries
c) Multiply the values of D's boundaries
d) Integrate the function over D

Answer 1

To find the area of the region D using a double integral, follow these steps: define the bounds of D, set up a double integral, and integrate over D.

Step-by-step explanation:

To find the area of the region D using a double integral, follow these steps:

1. Define the bounds of the region D in terms of x and y.
2. Set up a double integral with the function 1 as the integrand and the bounds of D.
3. Integrate the function 1 over D, which will give you the area of D.

For example, if the bounds of D are x = a to x = b and y = c to y = d, the double integral would be:

∫ ∫ 1 dA

Where the bounds of the integral are a to b for x and c to d for y.