How do I find the area of the region bounded by following?

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Homework Help Overview

The discussion revolves around finding the area of a region bounded by multiple functions, involving integrals and intersections of equations. Participants are exploring the complexities of setting up the problem, particularly with respect to the boundaries defined by the functions involved.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of integrals, questioning the coordinates of intersections and the implications of boundaries. There is a focus on whether to integrate over x or y, and the potential need to split the area into separate regions for calculation.

Discussion Status

The discussion is active, with participants providing guidance on how to approach the problem. There are multiple interpretations being explored, particularly regarding the setup of integrals and the identification of intersections. Some participants express confusion over the original poster's approach, indicating a need for clarification.

Contextual Notes

There are mentions of previous problems and the original poster's experience level, suggesting that this problem may be more complex than earlier ones. The requirement of "x is greater than or equal to zero" is noted as a point of confusion regarding its relevance to the problem setup.

Drioton
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Homework: Misplaced Thread -- Member warned to post homework questions in the appropriate area
Using integrals, consider the 7 requirements:
Any my attempted solution that I have no idea where I am going:
And the other one provides the graph:
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I'm not sure what you did in your approach besides rewriting the equations and it is difficult to read or understand.

This shouldn't be the first "find the area" problem you encounter. How did you solve the previous problems?

You have marked two intersections of the different equations already. What are their coordinates? Where is a third intersection at the boundary of your area?

You can integrate over x or over y. How would you set up the integrals? Which one looks easier?
 
mfb said:
I'm not sure what you did in your approach besides rewriting the equations and it is difficult to read or understand.

This shouldn't be the first "find the area" problem you encounter. How did you solve the previous problems?

You have marked two intersections of the different equations already. What are their coordinates? Where is a third intersection at the boundary of your area?

You can integrate over x or over y. How would you set up the integrals? Which one looks easier?
F07813A0-8387-4907-89FA-876E87CFD491.jpeg

Here, but these two problems are different. they only consist of one function. Whereas this question has “x is greater than or equal to zero” (what is the meaning of this with respect to the problem) part, and has two functions. Besides the solution in yellow paper, it is unclear how I figure these out?
 
You could rotate your images in the correct orientation, that would help already.
Drioton said:
Here, but these two problems are different. they only consist of one function.
It is still the area between four boundary lines. Here you just have three.

In one of the two options for the integration it is advisable to split the area into two regions, calculate their area separately and then add them. In the other case (the easier one!) this is not necessary.
 

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