I need to find the length of the curve y=(1/2)x^2 - (1/4)lnx between x=1 and x=8.

I derived it and squared it and added one to it so now I'm left with the integral from 1 to 8 of sqrt (x^2 + (1/2) + 1/16x^2) dx. How do I integrate this?

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- Nov 24th 2008, 06:56 PMelitespartLength between curve
I need to find the length of the curve y=(1/2)x^2 - (1/4)lnx between x=1 and x=8.

I derived it and squared it and added one to it so now I'm left with the integral from 1 to 8 of sqrt (x^2 + (1/2) + 1/16x^2) dx. How do I integrate this? - Nov 24th 2008, 07:23 PMo_O

Now, as you found:

So:

So, taking the square root and our final integral becomes: - Nov 24th 2008, 07:23 PMSoroban
Hello, elitespart!

Quote:

Find the length of the curve: . between and

I derived it and squared it and added one to it.

So now I'm left with: .

How do I integrate this?

*perfect square*under the radical . . .

. . see?

- Nov 24th 2008, 07:26 PMelitespart
Awesome! Thanks a lot guys.

- Nov 24th 2008, 07:38 PMKrizalid
It's actually but note that for hence