Drawing domain of R^2 integral

In summary, the bounds for the given integral are x starting at 1/e and ending at 1/y, where 1/e is a constant and x=1/y is a rectangular hyperbola in the first quadrant. The domain is bounded by the curves y=1, y=e, and x=1/y, with points of intersection at (1/e, 1), (1/e, e), and (1, 1).
  • #1
Jerbearrrrrr
127
0
[tex]\int _1 ^e \int _{1/e} ^{1/y} f dx dy[/tex]
If asked how to sketch the bounds for that:

"x starts at x=1/e and ends at x=1/y
1/e is just a constant so that's a straight line
and x=1/y is the exact same line as y=1/x"

That's a decent enough engineer's explanation right?
(no one in university should need the y-bounds explained)
 
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  • #2
well, y=1/x is not a straight line,it's a rectangular hyperbola present in 1st and 4th quadrant,but we have to consider only 1st quadrant as limits of x and y are +ive.
 
  • #3
The domain in the first quadrant is bounded by the curves y = 1, y = e and x = 1/y.
The points of intersection are (1/e, 1), (1/e, e) and (1, 1).
 

FAQ: Drawing domain of R^2 integral

What is the "Drawing domain of R^2 integral"?

The "Drawing domain of R^2 integral" refers to the process of graphically representing the area under a two-dimensional function using integration. It involves finding the limits of integration and using them to draw the appropriate region on the x-y plane.

How is the "Drawing domain of R^2 integral" different from a regular integral?

The "Drawing domain of R^2 integral" is a specific type of integral that deals with two-dimensional functions and represents the area under the curve. In contrast, a regular integral can be used to find the area under any type of function, including one-dimensional functions.

Why is the "Drawing domain of R^2 integral" important in science?

The "Drawing domain of R^2 integral" is important in science because it allows us to represent and analyze complex two-dimensional functions and their areas. It is commonly used in physics, engineering, and other scientific fields to solve problems involving areas and volumes.

What are the steps involved in "Drawing domain of R^2 integral"?

The first step is to identify the function and its limits of integration. Then, plot the function on the x-y plane and shade the area under the curve. Next, determine the limits of integration on the x-axis and use them to find the corresponding limits on the y-axis. Finally, integrate the function with respect to x to find the area under the curve.

Are there any limitations to the "Drawing domain of R^2 integral" method?

Yes, there are some limitations to the "Drawing domain of R^2 integral" method. It can only be used for two-dimensional functions, and it may not work for some irregular or complex functions. Additionally, the accuracy of the drawn area depends on the precision of the graph and the integration method used.

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