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Arc length Formula
L = ∫ ds
Where
ds √ (1+ (dy/dx)2 ) dx if y = f(x), a < x < b
ds √ (1+ (dx/dy)2 ) dy if x = h(y), c < y < d
Note that there is no limits were put on the integral as the limits will depend on the ds that we are using. By using the first ds will need x limits of integration and by using the second ds will need y limits of integration.
Idea of the arc length formula as a single integral with dissimilar ways to define ds will be suitable when we run across arc lengths in future sections. As well, this ds notation will be a nice notation for the later section as well.
Product and Quotient Rule : Firstly let's see why we have to be careful with products & quotients. Assume that we have the two functions f ( x ) = x 3 and g ( x ) = x 6 .
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in right angle triangle BAC.
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