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September 7th, 2008, 01:03 PM  #1 
Newbie Joined: Sep 2008 Posts: 4 Thanks: 0  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. 
September 7th, 2008, 01:54 PM  #2 
Guest Joined: Posts: n/a Thanks:  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 
Senior Member Joined: May 2007 Posts: 402 Thanks: 0  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... 
September 7th, 2008, 02:04 PM  #4 
Newbie Joined: Sep 2008 Posts: 4 Thanks: 0  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. 
September 7th, 2008, 02:19 PM  #5 
Guest Joined: Posts: n/a Thanks:  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 
Newbie Joined: Sep 2008 Posts: 4 Thanks: 0  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

September 7th, 2008, 04:28 PM  #7 
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  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.

September 11th, 2008, 09:55 AM  #8 
Newbie Joined: Sep 2008 Posts: 4 Thanks: 0  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. 
September 11th, 2008, 11:43 AM  #9  
Senior Member Joined: Jul 2008 Posts: 895 Thanks: 0  Re: Need help on an arc length of curve problem Quote:
 

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