## jocelynevsq 2 years ago find the region bounded by the graph of y^2=x^2-x^4

1. amistre64

what does your graph look like?

2. jocelynevsq

|dw:1359922854861:dw|

3. jocelynevsq

i'm not sure

4. jocelynevsq

wait nevermind it's not that

5. amistre64

|dw:1359922919356:dw| thats what i was thinking it was like

6. jocelynevsq

yes

7. amistre64

then the only pertinent equations are: x^2-x^4 and y=-sqrt(x)

8. amistre64

they meet at x=0, and what is the other x value?

9. jocelynevsq

I don't know

10. amistre64

-sqrt(x) = x^2 - x^4 0 = x^2 -sqrt(x) -x^4 that does seem a bit convoluted :/

11. ZeHanz

Here's the graph:

12. amistre64

hmmm, that is one representation i can see of it :)

13. amistre64

so if thats the case, would changing it to parametric form help out?

14. ZeHanz

I'd: Write y as function of x: y=xsqrt(1-x²) Integrate using u=1-x² Multiply by 4, because of the symmetry...

15. amistre64

sounds crazy enough to work :)

16. jocelynevsq

what do I multiply by 4?

17. ZeHanz

If you integrate as I did, you only get the area between the positive x-axis and the graph (upper right part of the whole thing) There a 4 such areas, so multiply by 4.

18. jocelynevsq

oh okay thanks

19. ZeHanz

I've got to 8/3, hope this helps ;)

20. jocelynevsq

thanks!