Question: Suppose f is continuous, f(0) = 0, f(1) =1, f'(x) > 0, and ∫01f(x)dx = 1/3. Find the value of the integral of f-1(y)dy One solution is to assess the function as if it were a function of y. I understand that method and have arrived at the answer. But I am curious to see if there is another solution since I have been unable to come up with another method besides just looking at the graph visually after I rotate it. If there is a more general answer to assessing the integral of inverse functions, that would be great if you could provide an explanation as well! Also, if you were asked to solve this: ∫01 d/dx f-1(y)dy, is it possible with the information given above alone? If not, what additional information is necessary? Also, are there any general rules when integrating inverse functions? Thank you so much!