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## Calculus 2

### Course: Calculus 2>Unit 4

Lesson 13: Arc length

# Worked example: arc length (advanced)

A worked example of finding arc length using definite integrals. This example involves some challenging algebra.

## Want to join the conversation?

• Here's the thing, I figured out this problem on my own without help, but it took me an hour. It took me 3 pages of re-writing the problem to figure out that I can take the problem out of the square root, then I watch the video and a couple minutes into the problem he's just like "oh btw this can be taken out of the square root" So naturally my question is: Is there some sort of pattern I'm not seeing or does this just come from practice and experience, because I'm starting to get a little discouraged •  Don't be discouraged. What you just did, figuring it out on your own, is worth 10 videos. You can watch as much as you want, but without PRACTICE, you won't get anywhere. I wish more students would spend that kind of time trying to figure things out - that is how your mathematical intuition and situation recognition grows. I prefer to use the phrase "situation recognition" rather than "pattern recognition", because patterns are too specific - if the pattern does not match exactly to what you have seen, you may pass over the similarity of the current situation to a previously encountered situation and abandon your investigation prematurely.

So keep watching videos, do the exercises, prove results to yourself, then, if all that fails, ask for help, everyone here has asked for help in math at one time or another. Just remember to be prepared to explain what you have tried when you ask for help - that way we can see you have been honest in your attempt to figure it out on your own.
• What is the practical use of calculating arc lengths? •  My professor said that he was an electrical engineer and used it while working on the cable harness in cars. He had to calculate how long a wire had to be, and know the exact length, so that if anyone else needed to look at his measurements, they would be precise. So essentially, you can find the exact length of arcs or even curved objects in the real world.
• I dont understand how he got the square of the derivative. I understand that the 1 + f'(x) is from the formula, but how is (1/2 x^2 - 1/2 x^-2) squared equal to (1/4 x^4 - 1/2 + 1/4 x^-4) ? • Will calculating arc length prove useful in calculating surface area of objects? • How did Sal know what x^8+2x^4+1 = (x^4+1)^2?
Is there a shortcut involved, or maybe a trick?
Is there a formula to find out how x^8+2x^4+1 = (x^4+1)^2 ? • at sal finished up the equation. the next equation he left out the 1 on the right side of the equation? I thought he canceled out the 1's on both sides, but the 1 on the left hand side appears at when he brings us up to speed with what he's done so far. what happened to the 1 on the right hand side of the equation at ? • Find the area of the subtending arc when () = 30° and r = 6.
can we do this using integration?if possible,how?
(1 vote) • Why is the beginning function, f(x)=x^3/6+1/2x, almost identical to x^3/6-1/2x, the equation Sal finds at ?   