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Math Help - Integrals (Top - Bottom)

  1. #1
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    Post Integrals (Top - Bottom)





    For this problem I understand how to do everything.

    For the green (Square root of X is first because it is LEFT on the Graph. and they negative the (X/3) because it is on the RIGHT of the Graph.

    But why is it for the answer highlighted in BLUE. Why is it (3y - (Y^2))?

    Shouldn't it be ((Y^2) - 3Y)? Since (Y^2) is on TOP?

    Aren't I suppose to use Top - Bottom on this?
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  2. #2
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    You have to remember that top and bottom are relative when integrating. In the blue box, you're solving for y, so you have to sort of turn your head to the right and view the graph in terms of y. By doing so, you will see that the top graph (in terms of y) is actually 3y and the bottom graph (in terms of y) is y^2. Does it make more sense now?
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  3. #3
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    Quote Originally Posted by Brazuca View Post

    Aren't I suppose to use Top - Bottom on this?
    Yep.

    Quote Originally Posted by Brazuca View Post

    But why is it for the answer highlighted in BLUE. Why is it (3y - (Y^2))?

    Shouldn't it be ((Y^2) - 3Y)? Since (Y^2) is on TOP?
    y^2 is not on top. Consider rotating the graph 90 degrees to the right.
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  4. #4
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    Well, the basic is to see which part cover the larger area and which part cover the smaller area, not top-bottom or right - left

    For the blue one : because the integral is (dy), it means that you see the area bounded by the curves and the y-axis.

    The straight line covers the larger area from 0 to 3 in y-axis than y^2 = x
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  5. #5
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    Oh I get it I tilt my head to the side to see it.

    So Top - Bottom is different when its in the Area of something than when it is the Volume of a solid.
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