The curve y=f(x) called Tractrix has the following property" the derivative at any point x satisfies the formula: f'(x) = -f(x) (1-f(x)^2)^(1/2) Consider the region under the tractrix, within the limits 0

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) (1-f(x)^2)^(1/2) 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-sunstitution]

anonymous · Answer

i got f(x) = .5(2(1-f(a)^2))^(1/2)-2(1-f(0)^2)^(1/2)
but i don't know what f(0) is