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jocelynevsq

  • 2 years ago

find the region bounded by the graph of y^2=x^2-x^4

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  1. amistre64
    • 2 years ago
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    what does your graph look like?

  2. jocelynevsq
    • 2 years ago
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    |dw:1359922854861:dw|

  3. jocelynevsq
    • 2 years ago
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    i'm not sure

  4. jocelynevsq
    • 2 years ago
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    wait nevermind it's not that

  5. amistre64
    • 2 years ago
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    |dw:1359922919356:dw| thats what i was thinking it was like

  6. jocelynevsq
    • 2 years ago
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    yes

  7. amistre64
    • 2 years ago
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    then the only pertinent equations are: x^2-x^4 and y=-sqrt(x)

  8. amistre64
    • 2 years ago
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    they meet at x=0, and what is the other x value?

  9. jocelynevsq
    • 2 years ago
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    I don't know

  10. amistre64
    • 2 years ago
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    -sqrt(x) = x^2 - x^4 0 = x^2 -sqrt(x) -x^4 that does seem a bit convoluted :/

  11. ZeHanz
    • 2 years ago
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    Here's the graph:

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  12. amistre64
    • 2 years ago
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    hmmm, that is one representation i can see of it :)

  13. amistre64
    • 2 years ago
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    so if thats the case, would changing it to parametric form help out?

  14. ZeHanz
    • 2 years ago
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    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
    • 2 years ago
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    sounds crazy enough to work :)

  16. jocelynevsq
    • 2 years ago
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    what do I multiply by 4?

  17. ZeHanz
    • 2 years ago
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    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
    • 2 years ago
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    oh okay thanks

  19. ZeHanz
    • 2 years ago
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    I've got to 8/3, hope this helps ;)

  20. jocelynevsq
    • 2 years ago
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    thanks!

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