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September 7th, 2008, 01:03 PM   #1
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Need help on an arc length of curve problem

The problem says to find the length of the arc of the parabola from (0,0) to (1,1).
When I work it I end up with crazy (for my math level) integrals that don't seem right for the problem.
When working it from I get
That makes me do integration by parts, and this problem is from before that section.
Working the problem from I get and that doesn't seem right either.
Any help on how to work this problem is greatly appreciated.
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September 7th, 2008, 01:54 PM   #2
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Re: Need help on an arc length of curve problem

I think I found a relatively easy way to integrate this.

We have

Now, let

Change the limits of integration to 0 to 4.



Now, let

This gives:



Believe it or not, this whittles down to:



Now, use the limits of integration.
 
September 7th, 2008, 02:03 PM   #3
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Re: Need help on an arc length of curve problem

The second one is easy. Just replace . Then you have:



You can do this on your own from now...
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September 7th, 2008, 02:04 PM   #4
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Re: Need help on an arc length of curve problem

Holy cow! That is crazy lol, seems a little above my level. Maybe my problem is getting the actual integral? This is a problem for me to review prior to the test, but we haven't learned most of the stuff you just did.

We just started integration by parts, and we haven't gotten into trigonometric integral solutions. I think I may have just came up with the wrong integrals for the problem.
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September 7th, 2008, 02:19 PM   #5
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Re: Need help on an arc length of curve problem

No, that's the right integral. Arc length for from 0 to 1 would be

The general formula is and that is what you have.
 
September 7th, 2008, 02:50 PM   #6
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Re: Need help on an arc length of curve problem

Oh man, this problem is just nasty then lol, thank you very much for the help
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September 7th, 2008, 04:28 PM   #7
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Re: Need help on an arc length of curve problem

Hopefully not intruding on this fine work, but my first thought would be that it is the same length as that for y = x^2. Same trig mess though.
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September 11th, 2008, 09:55 AM   #8
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Re: Need help on an arc length of curve problem

We went over this "hw" problem in class... The teacher said for us, not having learned trig substitution yet, that it is impossible to solve. Why would a teacher assign a hw problem that is impossible to solve, so we learn how it feels to be demoralized?

Thanks for the help though.
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September 11th, 2008, 11:43 AM   #9
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Re: Need help on an arc length of curve problem

Quote:
Originally Posted by Prometheos
Why would a teacher assign a hw problem that is impossible to solve, so we learn how it feels to be demoralized?
Good Lord, no! You are surely not the only student in that class, and your teacher is surely not a mind-reader. He/she will begin to recognise capabilities as the year proceeds, but there are always those who rise to a challenge. He/she has to care for all needs, not just yours. If not presented with such challenges now an then, some complain [because they are "bright", of course] that they are not challenged enough. Well, you can please some of the people some of the time .... . The motive might be for you to do some research into future studies. I see absolutely nothing wrong with that since most students seriously studying calculus do so because they are fairly good at it at least, and are ambitious.
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