well this is what i think....if you graph the function and visualize the rotation you will see that it is finite.
Hmm this question is kind of werid. I'm not sure how to tackle it.
Suppose that a water jug is made by rotating the curve x = [(1-y)^-(1/4)]*[(2-y)^(-1/6)] about the y-axis from y = -infinity to y = 0. Determine if this jug can hold a finite or infinite volume of water. Explain why. Do not try to evaluate the integral.