- #1
Integral: x = y^2 - Solving the Mystery
- Thread starter Miike012
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- Integral
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Homework Help Overview
The discussion revolves around the function defined by the equation x = y^2 and its relationship to y = x^(1/2). Participants are exploring the implications of these equations in the context of integrals and area calculations under curves.
Discussion Character
- Conceptual clarification, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- Participants are questioning the equivalence of the two forms of the function and exploring the reasoning behind the choice of one representation over the other. There are suggestions to graph the functions to visualize their relationship, and inquiries about squaring both sides of the equation.
Discussion Status
The discussion is active, with participants providing insights and asking clarifying questions. Some guidance has been offered regarding the implications of graphing the functions and the need to consider the inversion of the function when calculating areas under the curve.
Contextual Notes
There is mention of calculating areas using integrals, with a focus on the relationship between the original function and its inverted form. Participants are also considering the implications of swapping axes in their calculations.
- #2
Frogeyedpeas
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Why don't you see if those two are equal?
Try graphing them both
Try graphing them both
- #3
I like Serena
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MHB
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Hi Miike012! 
What do you get if you square both sides of y = x1/2?
What do you get if you square both sides of y = x1/2?
- #4
Miike012
- 1,009
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Ok yes that's true.. I guess what I am really asking my self is why did they go with x = y^2 instead of y = x^1/2.
- #5
I like Serena
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Can I assume this is about integrals?
The white area is calculated using the integral of y(x)=x1/2.
This integral calculates the area between the graph and the x-axis.
To calculate the gray area, basically the axes are swapped around, so the integral between the graph and the y-axis can be calculated.
But if you do that, the function has to be inverted as well.
The white area is calculated using the integral of y(x)=x1/2.
This integral calculates the area between the graph and the x-axis.
To calculate the gray area, basically the axes are swapped around, so the integral between the graph and the y-axis can be calculated.
But if you do that, the function has to be inverted as well.
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