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Arc Length for Parametric Equations
L = ∫βα √ ((dx/dt)2 + (dy/dt)2) dt
Note: that we could have utilized the second formula for ds above is we had supposed instead that
dy/dt > 0 for α < t < β
If we had moved out this route in the derivation we would have gotten similar formula.
Examples on Log rules: Example: Calculate (1/3)log 10 2. Solution: log b n√A = log b A 1/n = (1/n)log b A (1/3)log 10 2 = log 10 3 √2 = log 10 1.
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