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Math Help - area

  1. #1
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    area

    Find the area of the region bounded by the y-axis, the curve y=x^3
    and the lines y=1 and y=27
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  2. #2
    Senior Member Peritus's Avatar
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    <br />
\int\limits_1^{27} {\sqrt[3]{y}dy}  = 60
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  3. #3
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    Hello, gracey!

    peritus is absolutely correct . . .


    Find the area of the region bounded by the y-axis, the curve y\:=\:x^3
    and the lines y=1 and y=27.
    Did you make a sketch?
    Code:
              |
            27+-----------*
              |:::::::::::
              |::::::::::*
              |::::::::::
              |:::::::::*
              |::::::::*
             1+------*
              |   *
          - - * - - - - - - - -
          *   |
       *      |
     *        |
    *         |

    It is easier to integrate with respect to y\!:\;\;x \:=\:y^{\frac{1}{3}}


    So we have: . A \;=\;\int^{27}_1\,y^{\frac{1}{3}}\,dy

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  4. #4
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    Just a sketch...
    Attached Thumbnails Attached Thumbnails area-area_cropped.png  
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  5. #5
    Super Member wingless's Avatar
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    It's even easier if you calculate
    3\cdot27 - \int^{3}_{1} x^3~dx - 1
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  6. #6
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    thankyou
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