If one region is above the $x$-axis, and the other below it, should “the ratio of their areas” use...












3












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Good morning mathematicians,



I apologize for asking such a basic question. When you are to find the ratio of "Area 1" and "Area 2", such that "Area 1" is the area of a region above the x-axis and "Area 2" is the area of a region below the x-axis, are you looking for an absolute value of the ratio, or do you leave the value negative?










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  • 2




    $begingroup$
    It depends on context. After all, treating below-the-$x$-axis regions as having negative area is a key element in how integration works, so "maybe" the ratio here should be considered negative if this is an integration exercise. On the other hand, if you simply happen to be using integration as a means of computing the areas of a couple of geometric figures, one of which just happens to be below the $x$-axis, then it's likely that "area" should be taken in absolute value. Authors sometimes avoid confusion by writing, say, "the ratio of the signed areas".
    $endgroup$
    – Blue
    Jan 13 at 8:28


















3












$begingroup$


Good morning mathematicians,



I apologize for asking such a basic question. When you are to find the ratio of "Area 1" and "Area 2", such that "Area 1" is the area of a region above the x-axis and "Area 2" is the area of a region below the x-axis, are you looking for an absolute value of the ratio, or do you leave the value negative?










share|cite|improve this question











$endgroup$








  • 2




    $begingroup$
    It depends on context. After all, treating below-the-$x$-axis regions as having negative area is a key element in how integration works, so "maybe" the ratio here should be considered negative if this is an integration exercise. On the other hand, if you simply happen to be using integration as a means of computing the areas of a couple of geometric figures, one of which just happens to be below the $x$-axis, then it's likely that "area" should be taken in absolute value. Authors sometimes avoid confusion by writing, say, "the ratio of the signed areas".
    $endgroup$
    – Blue
    Jan 13 at 8:28
















3












3








3





$begingroup$


Good morning mathematicians,



I apologize for asking such a basic question. When you are to find the ratio of "Area 1" and "Area 2", such that "Area 1" is the area of a region above the x-axis and "Area 2" is the area of a region below the x-axis, are you looking for an absolute value of the ratio, or do you leave the value negative?










share|cite|improve this question











$endgroup$




Good morning mathematicians,



I apologize for asking such a basic question. When you are to find the ratio of "Area 1" and "Area 2", such that "Area 1" is the area of a region above the x-axis and "Area 2" is the area of a region below the x-axis, are you looking for an absolute value of the ratio, or do you leave the value negative?







integration ratio






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edited Jan 13 at 8:21









Blue

49.1k870156




49.1k870156










asked Jan 13 at 8:15









Adam PáltikAdam Páltik

1149




1149








  • 2




    $begingroup$
    It depends on context. After all, treating below-the-$x$-axis regions as having negative area is a key element in how integration works, so "maybe" the ratio here should be considered negative if this is an integration exercise. On the other hand, if you simply happen to be using integration as a means of computing the areas of a couple of geometric figures, one of which just happens to be below the $x$-axis, then it's likely that "area" should be taken in absolute value. Authors sometimes avoid confusion by writing, say, "the ratio of the signed areas".
    $endgroup$
    – Blue
    Jan 13 at 8:28
















  • 2




    $begingroup$
    It depends on context. After all, treating below-the-$x$-axis regions as having negative area is a key element in how integration works, so "maybe" the ratio here should be considered negative if this is an integration exercise. On the other hand, if you simply happen to be using integration as a means of computing the areas of a couple of geometric figures, one of which just happens to be below the $x$-axis, then it's likely that "area" should be taken in absolute value. Authors sometimes avoid confusion by writing, say, "the ratio of the signed areas".
    $endgroup$
    – Blue
    Jan 13 at 8:28










2




2




$begingroup$
It depends on context. After all, treating below-the-$x$-axis regions as having negative area is a key element in how integration works, so "maybe" the ratio here should be considered negative if this is an integration exercise. On the other hand, if you simply happen to be using integration as a means of computing the areas of a couple of geometric figures, one of which just happens to be below the $x$-axis, then it's likely that "area" should be taken in absolute value. Authors sometimes avoid confusion by writing, say, "the ratio of the signed areas".
$endgroup$
– Blue
Jan 13 at 8:28






$begingroup$
It depends on context. After all, treating below-the-$x$-axis regions as having negative area is a key element in how integration works, so "maybe" the ratio here should be considered negative if this is an integration exercise. On the other hand, if you simply happen to be using integration as a means of computing the areas of a couple of geometric figures, one of which just happens to be below the $x$-axis, then it's likely that "area" should be taken in absolute value. Authors sometimes avoid confusion by writing, say, "the ratio of the signed areas".
$endgroup$
– Blue
Jan 13 at 8:28












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$begingroup$

Typically, areas are always non-negative numbers, so a ratio of areas should also be non-negative (i.e. if the result is negative, the absolute value is taken).






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    1 Answer
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    1 Answer
    1






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    active

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    active

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    3












    $begingroup$

    Typically, areas are always non-negative numbers, so a ratio of areas should also be non-negative (i.e. if the result is negative, the absolute value is taken).






    share|cite|improve this answer









    $endgroup$


















      3












      $begingroup$

      Typically, areas are always non-negative numbers, so a ratio of areas should also be non-negative (i.e. if the result is negative, the absolute value is taken).






      share|cite|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        Typically, areas are always non-negative numbers, so a ratio of areas should also be non-negative (i.e. if the result is negative, the absolute value is taken).






        share|cite|improve this answer









        $endgroup$



        Typically, areas are always non-negative numbers, so a ratio of areas should also be non-negative (i.e. if the result is negative, the absolute value is taken).







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Jan 13 at 8:20









        Parcly TaxelParcly Taxel

        44.6k1376109




        44.6k1376109






























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