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Integral: x = y^2 - Solving the Mystery
- Thread starter Miike012
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In summary, the conversation is discussing the equation x = y^2 and y = x^1/2 and their relationship to calculating the white and gray areas using integrals. The question is raised about why x = y^2 is used instead of y = x^1/2 and the concept of inverting the function is explained. The conversation ends with a suggestion to graph both equations.
- #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?
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Miike012
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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.
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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.
FAQ: Integral: x = y^2 - Solving the Mystery
What is the concept of "Integral: x = y^2 - Solving the Mystery"?
The concept of "Integral: x = y^2 - Solving the Mystery" is a mathematical problem that involves using integration to solve for the unknown variable, x, in an equation where the other variable, y, is squared. It is often referred to as a "mystery" because it requires careful manipulation and use of integration techniques to arrive at a solution.
Why is it important to solve integrals?
Solving integrals is important because it allows us to find the area under a curve, which has a wide range of applications in fields such as physics, engineering, and economics. It also helps us to determine the value of a function at a specific point and allows us to solve a variety of mathematical problems.
What are the different integration techniques used to solve "Integral: x = y^2 - Solving the Mystery"?
Some common integration techniques used to solve "Integral: x = y^2 - Solving the Mystery" include substitution, integration by parts, and partial fractions. Each technique has its own set of rules and guidelines, and the choice of technique depends on the complexity of the integral and the available information.
Can "Integral: x = y^2 - Solving the Mystery" have multiple solutions?
Yes, "Integral: x = y^2 - Solving the Mystery" can have multiple solutions. This is because integration is a reverse process of differentiation, and there can be many different functions that have the same derivative. To find the correct solution, we must consider the given conditions and use appropriate integration techniques.
What are some real-life applications of "Integral: x = y^2 - Solving the Mystery"?
Some real-life applications of "Integral: x = y^2 - Solving the Mystery" include calculating the work done by a varying force, finding the center of mass of an object, and determining the velocity of an object with a changing acceleration. It is also used in fields such as economics and biology to model and analyze various phenomena.