# Double integral, find area

1. Aug 26, 2013

### Lorenc

"Hey guys, how are you? I was studying for my calculus final and stumbled upon a peculiar function.

1. The problem statement, all variables and given/known data

Now I have to find the area bounded by the function (x^2+y^2)^3=xy^4 using a double integral. Now, the problem is that the graph is totally unknown to me (I have some ideas but im not shure).

2. Relevant equations

(x^2+y^2)^3=xy^4

3. The attempt at a solution

A substitution with u and v, doesnt seem to work and going to polar doesnt work either :/ Maybe Im doing something wrong, I dont know. Can anybody help me? Thank you in advance :)

2. Aug 26, 2013

### dirk_mec1

Use polar coordinates.

3. Aug 26, 2013

### Lorenc

It doesnt seem to solve that way. Can you please write just the polar equation in this case?

4. Aug 26, 2013

### Ray Vickson

Just as a matter of terminology: you do not have a "function; you have two functions and one equation connecting them (to form a curve). At first I had a lot of trouble trying to decipher your post.

Certainly, a judicious change of variables makes the problem pretty straightforward.

5. Aug 26, 2013

### Lorenc

Two functions? Yes, but can the whole equation be plotted using the sepparate functions? Im sorry, but I really need to imagine the area of integration. And as for the change of variables, I was thinking u = x^2 + y^2, ok, but then?

6. Aug 29, 2013

### Jufro

I am attempting to do this problem, quick question just for clarity: is it x*y^4 of (x*y)^4?

7. Aug 29, 2013

### Zondrina

It is read $x*y^4$.

As for the problem, a simple change to polar co-ordinates is all that is needed.

8. Sep 10, 2013

### Lorenc

Thank you everyone :)