The curve y=f(x) called Tractrix has the following property: The derivative at any point x satisfies the formula:
f'(x) = -f(x)/
sqrt(1-(f(x))^2)
Consider the region under the tractrix, within the limits 0 =< x =< a. Find the volume of the solid obtained by revolving this region around the x-axis in terms of the constant c= f(a). [Hint: use u-sub].
The limitation of
algebra that leads development of calculus is that it can make a complex number
of variables present it as a single variable and then apply the necessary
formula needed to find the answer. After manipulation, the presented single
variable can be changed back to a complex variable by substitution
