# Area between two curves

1. May 6, 2013

### Saitama

1. The problem statement, all variables and given/known data
Consider curves $C_1: (y-x)=(x+y-\sqrt{2})^2$ and $C_2: (x+y-\sqrt{2})=(y-x)^2$, then the area between $C_1$ and $C_2$ is
A)1/2
B)1/3
C)1/4
D)None

2. Relevant equations

3. The attempt at a solution
Finding out the points of intersection would be a lot difficult here. And even if I find them, integration would be dirty. This is a question from my test paper and I suspect that it has an easy solution but I am unable to figure that out.

Any help is appreciated. Thanks!

Last edited: May 6, 2013
2. May 6, 2013

### Dick

Did you think about trying a change of variables?

3. May 6, 2013

### Saitama

Nope. How would I do that here? Substitute $y-x$ with $t$?

4. May 6, 2013

### Dick

Sure. Call x+y+sqrt(2)=s, x-y=t. Find the area is s,t coordinates. Don't forget the Jacobian factor.

5. May 6, 2013

### Saitama

Sorry, never heard of that before. :uhh:

Hmm...using the substitution, the question is similar to finding area between $y=x^2$ and $y^2=x$. The area between them is 1/3. This is the answer given in the answer key. Thank you Dick!

6. May 6, 2013

7. May 6, 2013