Calculating Curve Length: A Shortcut for Solving Complex Equations?

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    Curve Length
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Discussion Overview

The discussion revolves around finding the length of a specific curve defined by the equation $$y = \frac{{x}^{5}}{6} - \frac{lnx}{4}$$ over the interval from 2 to 4. Participants explore different methods for solving this problem, including integral calculus and numerical techniques.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant presents the problem and requests assistance in finding the curve length.
  • Another participant emphasizes the importance of showing progress in problem-solving to facilitate better assistance.
  • A participant shares their progress, specifically noting the integral that needs to be evaluated.
  • One participant suggests that numeric integration techniques may be necessary for solving the integral.
  • Another participant proposes that using a calculator could be the quickest way to arrive at a solution.

Areas of Agreement / Disagreement

There is no consensus on the best method to solve the problem, as participants suggest different approaches, including numeric integration and calculator use.

Contextual Notes

The discussion does not resolve the specific techniques for evaluating the integral, and assumptions about the methods' effectiveness remain unaddressed.

mathforsure
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Hi everyone, I have an exercise I haven't solved yet, please help me.
Find the length of the curve: $$y = \frac{{x}^{5}}{6} - \frac{lnx}{4}, 2 \le x \le 4$$.
 
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Hello and welcome to MHB, mathforsure! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
My progress, the last step is find the integral:
$$\int_{2}^{4}\sqrt{1 + (\frac{5x^{4}}{6} - \frac{1}{4x})^{2}}\,dx$$
 
I could be wrong, but it appears to me that you will need to use some sort of numeric integration technique. (Worried)
 
I think the fastest solution is using calculator (Wink)
 

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