My Math Forum Calculating Arc Length

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 February 26th, 2009, 06:55 PM #1 Newbie   Joined: Feb 2009 Posts: 1 Thanks: 0 Calculating Arc Length Hi, I have tried to do this problem for the last hour and Webassign is NOT liking my answer. Find the length of the arc: $y= 3 + \frac{1}{3} cosh(3x)$ on $0 \leq x \leq 3$ Here is what I got using the arc length formula: $\int\limits^{3}_{0} \sqrt{1 + sinh^2(3x)} dx$ $\int\limits^{3}_{0} 1 + sinh(3x)$ $= x - \frac{cosh(3x)}{3} |^{3}_{0}$ I get for my answer: $\frac{4}{3} cosh(9)$ which is the wrong answer. I don't think I'm doing these correctly. Can someone go through the steps?
February 27th, 2009, 06:29 PM   #2
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Re: Calculating Arc Length

Quote:
 Originally Posted by mollymcf2009 $\int\limits^{3}_{0} \sqrt{1 + sinh^2(3x)} dx$ $= \cancel{\int\limits^{3}_{0} 1 + sinh(3x) dx}$
Nope. You can't get rid of square roots that easily.

Use this instead: $sinh^2 a + 1= cosh^2 a$

(There are no further complications, as cosh is positive for real arguments.)

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