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patbatE21

  • 4 years ago

Integrate (9 - x^2 - x -1)dy from x = -1 to x = 2

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  1. TuringTest
    • 4 years ago
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    what problem exactly do you have with this integral?

  2. patbatE21
    • 4 years ago
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    well the I'm actually trying to sketch a region enclosed by given curves

  3. patbatE21
    • 4 years ago
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    but i think there is something wrong with my integration...so far I have 9y -1/3y^3 -1/2y^2 - y

  4. TuringTest
    • 4 years ago
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    first off I assume you mean (9 - x^2 - x -1)dx

  5. patbatE21
    • 4 years ago
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    yes

  6. TuringTest
    • 4 years ago
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    so then you answer is correct if you replace y's with x's

  7. patbatE21
    • 4 years ago
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    the actual question is " Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region

  8. patbatE21
    • 4 years ago
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    y = x + 1, y = 9 - x^2, x = -1, x = 2

  9. patbatE21
    • 4 years ago
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    I am just having issues finding the area

  10. TuringTest
    • 4 years ago
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    let's just do the integral first, yeah?

  11. patbatE21
    • 4 years ago
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    ok

  12. patbatE21
    • 4 years ago
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    I know that I will have to take the integral [f(y) -g(y)] from c to d

  13. TuringTest
    • 4 years ago
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    It's f(x)-g(x) I think you are having a problem keeping track of variables, remember y=f(x), so f(y) is something different and undefined here.

  14. patbatE21
    • 4 years ago
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    I believe that is my problem, understood

  15. TuringTest
    • 4 years ago
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    so your integral is\[\int\limits_{-1}^{2}9-x^2-x-1dx\]

  16. patbatE21
    • 4 years ago
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    Alright, I'm so far

  17. TuringTest
    • 4 years ago
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    your answer is right replaced with x's\[9x-{1\over3}x^3-{1\over2}x^2-x\]evaluated from -1 to 2, what do you get?

  18. patbatE21
    • 4 years ago
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    19.2

  19. TuringTest
    • 4 years ago
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    let me try! lol

  20. patbatE21
    • 4 years ago
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    lol ok

  21. TuringTest
    • 4 years ago
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    Sorry 19.5 Just the evaluation, right? As you see I hate that too, here's a site, if you don't already know it that's good for that. http://www.wolframalpha.com/ and here's your particular problem http://www.wolframalpha.com/input/?i=Integrate+%289+-+x%5E2+-+x+-1%29dx+from+-1+to+2

  22. patbatE21
    • 4 years ago
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    Thank you so much

  23. TuringTest
    • 4 years ago
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    wait a minute this is all wrong! I should have noticed sooner!

  24. patbatE21
    • 4 years ago
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    No its correct I just submitted it online and it is marked correct

  25. TuringTest
    • 4 years ago
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    did you mean it as you typed it? 9 - x^2 - x -1 are you mot missing an x? because 9-1=8 so the integration we di is wrong

  26. patbatE21
    • 4 years ago
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    yes thats correct

  27. patbatE21
    • 4 years ago
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    I see what you mean, but how is it still correct

  28. TuringTest
    • 4 years ago
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    Okay it's not ALL wrong, but the way wee did it is silly, it may be right, but we failed to notice that \[9 - x^2 - x -1=8-x^2-x\] So we integrated an extra term. It is important to see shortcuts like that, so at least look for those in the future :)

  29. patbatE21
    • 4 years ago
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    Ok, the ah-hah moments in math...such a wonderful subject

  30. patbatE21
    • 4 years ago
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    Thanks once again

  31. TuringTest
    • 4 years ago
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    very welcome!

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