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anonymous

  • 5 years ago

Find the area of the region bounded by the curves y=x^2 and x=y^2

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  1. amistre64
    • 5 years ago
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    double integral it ;)

  2. anonymous
    • 5 years ago
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    equal both equation to each other to find the boundaries:\[x^2 = x^{1\over2} \] Area of a bounded region:\[\int\limits_{a}^{b}Ytop - Ybottm dy\] where Ytop = which curve is the top part of the region Ybottom = curve that is the bottom part of the region a & b are the boundaries you found

  3. anonymous
    • 5 years ago
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    the curves intersect at (0,0) and (1/1) .... integrate x^(1/2) - x^2 between x=0 and x=1

  4. amistre64
    • 5 years ago
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    or simply see that the area is the region bound by the y = sqrt(x) and y=x^2 curves

  5. amistre64
    • 5 years ago
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    aash got it ;)

  6. amistre64
    • 5 years ago
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    Math did too lol

  7. anonymous
    • 5 years ago
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    alright thanks, know how to do regions between curves, just the x=y^2 is new and strange to me

  8. anonymous
    • 5 years ago
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    thanks amistre63

  9. anonymous
    • 5 years ago
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    whenever you have something like x=y^2 just solve for y to have a "normal" equation x=y^2 ==> y=x^(1/2)

  10. anonymous
    • 5 years ago
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    x=y^2 is same as y=x^(1/2)

  11. amistre64
    • 5 years ago
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    if we double integral it we would have to define a region for a domain and use z=0 as a starting point ;)

  12. anonymous
    • 5 years ago
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    y=+ or - sqrt(x) though doesnt it

  13. mathmagician
    • 5 years ago
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    ther are 2 points of intersection of functions- (0,0) and (1,1) Therefore area is\[\int\limits_{0}^{1}(\sqrt{x}-x^2)=1/3\]

  14. amistre64
    • 5 years ago
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    Ty; yes; but the -sqrt(x) is useless

  15. anonymous
    • 5 years ago
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    for area take + only

  16. anonymous
    • 5 years ago
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    area cannot be negative

  17. amistre64
    • 5 years ago
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    the left side of x^2 and the bottom of y=x^2 are pointless ;)

  18. amistre64
    • 5 years ago
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    if you get a negative area; take the absolute value to asdjust for errors in the way to subtracted

  19. anonymous
    • 5 years ago
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    ah ok thanks a lot everyone,

  20. anonymous
    • 5 years ago
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    haha and 1+1=2 :D

  21. anonymous
    • 5 years ago
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    the real reason for not taking the negative root is to make it a function

  22. amistre64
    • 5 years ago
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    5-3 = 2 3-5 = -2 ...just means you put them in the wrong order usually; so: |+-2| = 2

  23. anonymous
    • 5 years ago
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    ok great, thanks again

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