Question

The curve y = f(x) called Tractix, has the following property: the derivative at any point x satisfies the formula f'(x)=-f(x)/sqroot of (1-f(x)^2). Consider the region under the tractix 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-substitution.) f(0)=1 and f(a) = c.