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jedai17

  • 2 years ago

determine the limits and evaluate.. ∫∫x2y2dA where f is a figure bounded by F lines y = 1, y = 2 and x = 0, x = y

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  1. electrokid
    • 2 years ago
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    |dw:1364052128248:dw| that gives you the limits

  2. electrokid
    • 2 years ago
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    it is easier to travel on y-axis because there is no sudden breaks

  3. electrokid
    • 2 years ago
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    so \[0\le x\le y \qquad\text{&}\qquad1\le y\le2\]

  4. electrokid
    • 2 years ago
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    if you are on the x-axis, you have to consider two pieces A) \(1\le y\le2 \qquad\text{&}\qquad0\le x\le1\) B) \(x\le y\le2 \qquad\text{&}\qquad1\le x\le2\) and sum them

  5. electrokid
    • 2 years ago
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    follow?

  6. jedai17
    • 2 years ago
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    in x=y, the value of y will become a and 2?

  7. electrokid
    • 2 years ago
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    "a"?

  8. electrokid
    • 2 years ago
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    all points on the "x=y" line will have the same abscissa and ordinate

  9. jedai17
    • 2 years ago
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    ah ok..

  10. electrokid
    • 2 years ago
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    yup, in the problem, all you need are the limits

  11. jedai17
    • 2 years ago
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    will i add these A) 1≤y≤2&0≤x≤1 B) x≤y≤2&1≤x≤2 ??

  12. electrokid
    • 2 years ago
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    use the first method its easier.

  13. electrokid
    • 2 years ago
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    yes those are your two regions for the second method

  14. jedai17
    • 2 years ago
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    x=0 to 1 and y= 1 to 2 ?

  15. electrokid
    • 2 years ago
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    no x=0 to y and y=1 to 2

  16. electrokid
    • 2 years ago
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    |dw:1364053324530:dw|

  17. jedai17
    • 2 years ago
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    i will integrate x^2y^2 using the limits x=0 to y and y=1 to 2 ?

  18. electrokid
    • 2 years ago
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    methid "1" is the horizontal element method "2" is the vertical

  19. electrokid
    • 2 years ago
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    yep. you got it

  20. jedai17
    • 2 years ago
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    ah ok.. in \[\int\limits_{1}^{2}\int\limits_{0}^{y} x^2y^2 dxdy\], got 127/36.. is it right?

  21. electrokid
    • 2 years ago
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    \[ \int_{y=1}^2y^2\left[x^3\over3\right]_0^ydy={1\over3\times6}\left[y^6\right]_1^2 \]

  22. jedai17
    • 2 years ago
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    7/2?

  23. electrokid
    • 2 years ago
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    yep

  24. electrokid
    • 2 years ago
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    .. wait..

  25. jedai17
    • 2 years ago
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    ok..

  26. electrokid
    • 2 years ago
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    false alarm

  27. electrokid
    • 2 years ago
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    \[dA=dxdy\]

  28. electrokid
    • 2 years ago
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    kapeesh?

  29. jedai17
    • 2 years ago
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    127/36 = 3.53 7/2 = 3.5 my answer is 127/36 :)) its almost the same :)

  30. electrokid
    • 2 years ago
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    lol

  31. jedai17
    • 2 years ago
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    |dw:1364054668113:dw|

  32. jedai17
    • 2 years ago
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    @electrokid ? look at my answer?

  33. electrokid
    • 2 years ago
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    great job :D I'd personally not like to have many terms while integrating ... it gives migraine without it!

  34. jedai17
    • 2 years ago
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    thank you!so is my answer also correct?

  35. electrokid
    • 2 years ago
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    yep...

  36. jedai17
    • 2 years ago
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    thank you! tnx for ur time :)

  37. electrokid
    • 2 years ago
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    yer welcome :)

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