Find the area of the surface given by z = f(x, y) over the region R. (Hint: Some of the integrals are simpler in polar coordinates.) f(x, y) = 9 − x2 R: square with vertices (0, 0), (2, 0), (0, 2), (2, 2)

The area of the surface over R is

Step-by-step explanation:

From this study,

The surface area of f(x,y) is expressed by:

where

Given that:

f(x,y) = 9 - x²

Thus, and  

However, the area becomes:

From above, replacing x with

then

∴

Hence;

Therefore, the area of the surface over R is

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)

what do you mean by fog

step-by-step explanation: