Finding the Intersection of Two Graphs: Exact Solutions and Integrals

In summary: There is no closed form solution, you will need to use a numerical method. To indicate the upper bound, you can use a decimal place, or a symbol like a prime. Your integrals look okay.
  • #1
Jbreezy
582
0

Homework Statement



Hi I'm trying to find where these two graphs intersect I would like it to be exact but it isn't quite working.
If I have y = tan(x) and y = x^1/3 how can I solve exactly?

Homework Equations



tan(x) = x^1/3 ? Hmm.
I'm not sure. I don't want arctan popping up on the right side. So I don't know really.

The Attempt at a Solution

 
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  • #2
Jbreezy said:

Homework Statement



Hi I'm trying to find where these two graphs intersect I would like it to be exact but it isn't quite working.
If I have y = tan(x) and y = x^1/3 how can I solve exactly?

Homework Equations



tan(x) = x^1/3 ? Hmm.
I'm not sure. I don't want arctan popping up on the right side. So I don't know really.

The Attempt at a Solution


Show your work.
 
  • #3
I'm supposed to just set up the integral not evaluate it. They want me to consider y = tanx and y = x^1/3 in the first quadrant.
Rotated about x I have:
V = 2PI (integral) x(tanx-x^1/3) dx
Between what ever result I get for the intersection of 0 and tanx = x^1/3
and for about y I have
V = 2PI( integral) y(arctan(y) - y^3) dy
Between 0 and whatever y^3 = arctan(y) intersections is.
 
  • #4
This is my work
tan(x) = x^1/3
x = arctan(x^1/3) ok ... now I'm stuck
 
  • #5
Jbreezy said:
This is my work
tan(x) = x^1/3
x = arctan(x^1/3) ok ... now I'm stuck

That's because there is (very probably) no closed-form solution; just use a numerical method.
 
  • #6
What do you mean a numerical method and how am I supposed to indicate the upper bound my teacher gives 0's for decimals. Also does my integrals look OK?
 
  • #7
Do my integrals look set up properly? Also how am I supposed to write an upper limit? Like integral from 0 to
tan(x) = x^1/3? Because I can't really solve this but I have to represent it exactly.
 

FAQ: Finding the Intersection of Two Graphs: Exact Solutions and Integrals

What is "Intersection for integration"?

"Intersection for integration" is a term used in mathematics and science to describe the process of finding the commonalities between two or more sets of data or theories. It is often used to integrate different ideas or concepts in order to gain a better understanding of a particular phenomenon or problem.

How is "Intersection for integration" used in scientific research?

Scientists use "Intersection for integration" as a way to combine different theories or data sets in order to form a more comprehensive and accurate understanding of a particular topic. This method allows researchers to see connections and patterns that may not have been apparent when looking at each set of data separately.

What are some benefits of using "Intersection for integration"?

One of the main benefits of using "Intersection for integration" is that it allows scientists to form a more complete understanding of a topic by combining multiple perspectives or data sets. It can also help to identify gaps or inconsistencies in existing theories, leading to new discoveries or advancements in a particular field.

Are there any limitations to using "Intersection for integration"?

While "Intersection for integration" can be a useful tool in scientific research, it is important to note that it is not always appropriate or necessary. Some topics may not require the integration of multiple theories or data sets, and in some cases, it may not be feasible to do so. Additionally, the process of integration can be time-consuming and may require a significant amount of effort to ensure accuracy and consistency.

How can I apply "Intersection for integration" in my own scientific research?

If you are interested in using "Intersection for integration" in your own research, it is important to first identify the specific areas or topics where integration may be beneficial. This could involve looking for connections between different theories or data sets, or identifying gaps in existing research. It is also important to carefully consider the methods and techniques used in the integration process to ensure accuracy and validity of the results.

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