Calculating the area between two curves

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Homework Help Overview

The discussion revolves around calculating the area between the curves defined by the equations x=abs(y) and x=6-y^2. Participants are exploring how to set up the integral for this area calculation, particularly focusing on the integration limits and the treatment of the absolute value function.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss sketching the graphs to identify the positions of the curves relative to each other. There are attempts to determine the limits of integration based on intersection points and the behavior of the functions. Questions arise regarding the integration of the absolute value function and the correct identification of which function is above the other.

Discussion Status

The discussion is ongoing, with participants providing insights and seeking clarification on the limits of integration and the nature of the functions involved. Some guidance has been offered regarding the signum function, but there is no clear consensus on the correct approach to take.

Contextual Notes

Participants are navigating the complexities of integrating functions involving absolute values and are questioning their assumptions about the intersection points of the curves. There is a noted confusion regarding the identification of which function is above or below the other, impacting their setup for the integral.

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Homework Statement



Compute the area between the two functions as an integral along the x-axis or the y-axis:

x=abs(y)
x=6-y^2

Homework Equations





The Attempt at a Solution



I sketched the graph to determine which was to the right and which was left finding out that 6-y^2 is to the right then I found out where the limits of integration would be and go the to be +sqrt6 , -sqrt6 however I'm not getting the correct answer and I'm unsure of how to integrate the absolute value function, I tried to split it up into two separate integrals but it didn't work
 
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Ah, I see no I was not familiar with that function, I got my limits because those are the points where the parabola meets the y axis,
 
physstudent1 said:
Ah, I see no I was not familiar with that function, I got my limits because those are the points where the parabola meets the y axis,

But where does the curve intersect the line?
 
physstudent1 said:

Homework Statement



Compute the area between the two functions as an integral along the x-axis or the y-axis:

x=abs(y)
x=6-y^2

Homework Equations





The Attempt at a Solution



I sketched the graph to determine which was to the right and which was left finding out that 6-y^2 is to the right then I found out where the limits of integration would be and go the to be +sqrt6 , -sqrt6 however I'm not getting the correct answer and I'm unsure of how to integrate the absolute value function, I tried to split it up into two separate integrals but it didn't work

There isn't "one function to the right and the other to the left". There is one function above the other!
 

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