- #1

Shackleford

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3.b Find the arc length of the given curve

α(t) = (t, 1, (1/6)t^3 + (1/2)t^-1) from t = 1 to t = 3.

Of course, I need to find the first derivative and integrate its norm.

α'(t) = (1, 0, (1/2)t^2 - (1/2)t^-2)

∫ [1 + (1/4)t^4 + (1/4)t^-4]^(1/2) dt, t = 1 to t = 3.

Have I simply forgotten useful integrals?

5. Let α(t) = (e^t, e^-t, root2*t). Calculate first derivative, norm, and re-parametrize alpha by its arc length, starting at t = 0.

α'(t) = (e^t, -e^-t, root2)

∫ [e^2u + e^-2u + 2]^(1/2) du, u = 0 to u = t.