Calculating Area with Double Integrals - Solving for Unknown Functions

[Lorenc]

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

Homework Statement

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 I am not shure).

Homework Equations

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

The Attempt at a Solution

A substitution with u and v, doesn't seem to work and going to polar doesn't work either :/ Maybe I am doing something wrong, I don't know. Can anybody help me? Thank you in advance :)

 

[dirk_mec1]

Use polar coordinates.

 

[Lorenc]

It doesn't seem to solve that way. Can you please write just the polar equation in this case?

 

[Ray Vickson]

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

Homework Statement

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 I am not shure).

Homework Equations

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

The Attempt at a Solution

A substitution with u and v, doesn't seem to work and going to polar doesn't work either :/ Maybe I am doing something wrong, I don't know. Can anybody help me? Thank you in advance :)

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.

 

[Lorenc]

Two functions? Yes, but can the whole equation be plotted using the sepparate functions? I am 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?

 

[Jufro]

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

 

[STEMucator]

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

It is read $x*y^4$.

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

 

[Lorenc]

Thank you everyone :)