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Math Help - Finding the Area of an Enclosed Region

  1. #1
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    Finding the Area of an Enclosed Region

    How would I solve this problem...

    What is the area of the region enclosed by the graphs of f(x)=x-2x^2 and g(x)=-5x?
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  2. #2
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    Quote Originally Posted by summermagic View Post
    how would i solve this problem...

    What is the area of the region enclosed by the graphs of f(x)=x-2x^2 and g(x)=-5x?
    Finding the Area of an Enclosed Region-capture.jpg

    The area between curves is upper - lower

    \int_{0}^{3}(x-2x^2)-(-5x)dx=-2 \int_{0}^{3} (x^2-3x)dx...
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  3. #3
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    Hello, summermagic!

    I don't suppose you made a sketch . . .


    Find the area of the region enclosed by the graphs of f(x)=x-2x^2 and g(x)=-5x
    Code:
              |
          *   |
            * |  ..*..
        - - - *::::::::*- - - - - - -
            * | *::::::::*
           *  |   *:::::::*
              |     *::::::.
          *   |       *::::*
              |         *:::.
              |           *::
         *    |             *
              |

    The graphs intersect at (0,0) and (-3,-15).

    You must evaluate: . \int^3_0\bigg[(x-2x^2) - (-5x)\bigg]\,dx

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