Calculating Curve Length: A Shortcut for Solving Complex Equations?

In summary, the conversation discusses a math exercise involving finding the length of a curve. The curve is defined by the equation y = \frac{{x}^{5}}{6} - \frac{lnx}{4} and the interval 2 \le x \le 4. The user is asked to share their progress on the problem and they respond with the integral they have found so far. The conversation ends with a suggestion to use a numeric integration technique, such as a calculator, to solve the problem.
  • #1
mathforsure
3
0
Hi everyone, I have an exercise I haven't solved yet, please help me.
Find the length of the curve: \(\displaystyle y = \frac{{x}^{5}}{6} - \frac{lnx}{4}, 2 \le x \le 4\).
 
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  • #2
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?
 
  • #3
My progress, the last step is find the integral:
\(\displaystyle \int_{2}^{4}\sqrt{1 + (\frac{5x^{4}}{6} - \frac{1}{4x})^{2}}\,dx\)
 
  • #4
I could be wrong, but it appears to me that you will need to use some sort of numeric integration technique. (Worried)
 
  • #5
I think the fastest solution is using calculator (Wink)
 

FAQ: Calculating Curve Length: A Shortcut for Solving Complex Equations?

What is "Find the length of the curve"?

"Find the length of the curve" is a mathematical concept that involves determining the distance or length of a curved line or shape. It is often used in calculus, geometry, and other areas of mathematics.

Why is finding the length of a curve important?

Knowing the length of a curve can be useful in various real-world applications, such as engineering, architecture, and physics. It also helps in understanding the properties and behavior of curves in mathematical equations.

How do you find the length of a curve?

To find the length of a curve, you can use various mathematical methods such as the arc length formula, integration, or numerical approximation. The method used depends on the complexity of the curve and the available data.

What are some common types of curves that require finding their length?

Some common types of curves that require finding their length include circles, ellipses, parabolas, hyperbolas, and more complex curves such as spirals and fractals.

Are there any limitations to finding the length of a curve?

Yes, there are some limitations to finding the length of a curve. In some cases, the length of a curve may not have a finite value, making it impossible to calculate. Additionally, the accuracy of the calculated length may depend on the precision of the data and the method used for calculation.

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