Question

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].

Answer 1

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