Question

u
Y2+y +1
Evaluate 1
dx
1-COS X
COS X - COS X
Constant and o< X<x<T
Find the formic senics representing th​

Answer 1

Answer:

In Double Integrals over Rectangular Regions, we studied the concept of double integrals and examined the tools needed to compute them. We learned techniques and properties to integrate functions of two variables over rectangular regions. We also discussed several applications, such as finding the volume bounded above by a function over a rectangular region, finding area by integration, and calculating the average value of a function of two variables.

In this section we consider double integrals of functions defined over a general bounded region D on the plane. Most of the previous results hold in this situation as well, but some techniques need to be extended to cover this more general case.

General Regions of Integration

An example of a general bounded region D on a plane is shown in (Figure). Since D is bounded on the plane, there must exist a rectangular region R on the same plane that encloses the region D, that is, a rectangular region R exists such that D is a subset of R\left(D\subseteq R\right).

For a region D that is a subset of R, we can define a function g\left(x,y\right) to equal f\left(x,y\right) at every point in D and 0 at every point of R not in D.