- #1
Samuelb88
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Homework Statement
Find the arc length of y=e^x, from [0,1].
Homework Equations
The Attempt at a Solution
[tex]s = \int_0^1 (1 + e^2^x)^(^1^/^2^)dx[/tex]
I let t = e^x, dt=e^xdx; therefore dt/t=dx
[tex] s = \int_1^e \frac{(1+t^2)^(^1^/^2^)}{t}\right) dx[/tex]
Let t = tanT, dt = sec^2(T)dT (T for theta)
[tex] s = \int_{\frac{Pi}{4}\right)}^{arctan(e)} \frac{sec^3T}{tanT}\right)dT[/tex]
[tex] s = \int_{\frac{Pi}{4}\right)}^{arctan(e)} \frac{1/cos^3T}{sinT/cosT} \right) dT[/tex]
[tex] s = \int_{\frac{Pi}{4}\right)}^{arctan(e)} \frac{1}{sinT}\right) * \frac{1}{cos^2T} \right)dT[/tex]
Where do I go from here?
Any help would be greatly appreciated. :)
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