- #1

- 13

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Find the length of the curve

[tex] y = \frac{1}{2}(e^x + e^{-x}) , 0 \leq x \leq 2 [/tex]

Problem set up was easy enough

[tex] L= \int_0^2 \sqrt{ 1 + \frac{1}{4}( e^{2x} -2 + e^{-2x} ) } dx [/tex]

Looking back in my notes I see that the answer is

[tex] \frac{1}{2}( e^2 - e^{-2} ) [/tex]

But, how do you get there? I think my main problem is probably the algebra behind combing the 1 and derivative of y squared.