Is it possible to revolve a function around y = x? If so how would you do it? I suppose the main difficulty is in finding the radius for the area of a disk or cylinder. Is there any method that works will all or most functions?
Hi TheAbsoluTurk! Easiest way is to change to new coordinates p = x + y, q = x - y (or the same but divided by √2, if you prefer). Then x = y is the q axis, so that's just a rotation about the q axis.
Ok, let's say that I'm trying to rotate y = x^2 around y = x. p = x + y q = x - y So do I have to insert (q + y) into x to make y = (q + y)^2 ?
I understand that but I don't know what to do after that. Does r in ∏r^2 equal (p-q)/2? How do you integrate that?
no, the r is the distance from your axis your axis (originally called x=y) is the q axis, so r is the distance from the q axis, which is p (or is it p/2?)
Let me get this straight: What is the volume of y = x^2 rotated about y = x? Define p = x +y Define q = x - y I don't understand why you chose to insert x = (p+q)/2 and y = (p-q)/2 ? How did you get these?
(just got up :zzz:) first you convert everything into p and q then you solve the problem, in p and q (you've said you know how to do this) finally you convert your solution back to x and y