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anonymous

  • 5 years ago

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.

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  1. anonymous
    • 5 years ago
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    where are the curves?

  2. anonymous
    • 5 years ago
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    im attaching a file :) it had less than equal to signs and what not, so i just thought id attach the file

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  3. anonymous
    • 5 years ago
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    Okay so we first plot the functions

  4. anonymous
    • 5 years ago
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    http://www.wolframalpha.com/input/?i=Plot%5B {5-4cos%5Bx%5D%2Ccos%5Bx%5D}%5D{x%2C0%2CPi%2F2}%5D

  5. anonymous
    • 5 years ago
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    whoa, my graph was way off

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  6. anonymous
    • 5 years ago
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    no I think your right too

  7. anonymous
    • 5 years ago
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    ohh i see your graph has a bigger scale xD

  8. anonymous
    • 5 years ago
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    Yes, exactly

  9. anonymous
    • 5 years ago
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    okay, so can we set the two equations equal to eachother, to find the boundaries?

  10. anonymous
    • 5 years ago
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    actually, if we observe the graph, you see that they don't seem to have any intersection point between the interval 0, pi/2

  11. anonymous
    • 5 years ago
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    ooh i thought it intersected near the very beginning cuz it was so close lol

  12. anonymous
    • 5 years ago
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    Hold on

  13. anonymous
    • 5 years ago
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    kay. normally to find the boundaries of the two curves, you'd set them equal to eachother right? thats what i did with this problem and i ended up getting x = 0, and 2pi

  14. anonymous
    • 5 years ago
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    you are right it intersect at 0 http://www.wolframalpha.com/input/?i=Solve%5B5-4cos%5Bx%5D%3D%3Dcos%5Bx%5D%2Cx%5D

  15. anonymous
    • 5 years ago
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    The second part ask, should you integrate with respect to x or y what do you think?

  16. anonymous
    • 5 years ago
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    i think with respect to x. i honestly dont really know the difference, i usually integrate with respect to x lol ><

  17. anonymous
    • 5 years ago
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    Okay,it is a matter of convenience, you can do with either

  18. anonymous
    • 5 years ago
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    If we were to integrate with respect to x we can see that cos[x] is always below the other function

  19. anonymous
    • 5 years ago
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    However,it get tricker when you try to integrate with respect to y because for all y<1 you will need one integral and all y>1 you will need another integral Do you see why?

  20. anonymous
    • 5 years ago
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    is it because the y values for the upper (positive values) differ from the bottom (negative values) ?

  21. anonymous
    • 5 years ago
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    oh wait. is it because the highest y value cosx can go is either -1 or 1

  22. anonymous
    • 5 years ago
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    and for the other function, it can go higher than that

  23. anonymous
    • 5 years ago
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    When you are integrating with respect to x what you are doing is adding up infinite number of verticle strip between two functions from x=0 to x=pi/2

  24. anonymous
    • 5 years ago
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    how about when you integrate with respect to y?

  25. anonymous
    • 5 years ago
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    Go here http://www.twiddla.com/537036

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