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Math Help - Area of region of plane between the graph

  1. #1
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    Area of region of plane between the graph

    Find the area of the region of the plane between the graphs of
    y=9-x^2 and
    y=1+2x

    would f(x)=9-x^2
    and g(x)=1+2x

    and then set them equal? 9-x^2=1+2x

    confused on how to do this problem
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  2. #2
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    Quote Originally Posted by Jim Marnell View Post
    Find the area of the region of the plane between the graphs of
    y=9-x^2 and
    y=1+2x

    would f(x)=9-x^2
    and g(x)=1+2x

    and then set them equal? 9-x^2=1+2x

    confused on how to do this problem
    9-x^2 = 1+2x

    0 = x^2+2x-8

    0 = (x+4)(x-2)

    intersection points are x = -4 and x = 2

    A = \int_{-4}^2 (9-x^2) - (1+2x) \, dx

    simplify the integrand, integrate, and use the FTC to find the area.
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  3. #3
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    I'm not sure how to simplify the integrand, probably because im not sure what it means to do that but i can integrate and perform the Fundamental Theorum. Can any1 show me how to simplify the integrand
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  4. #4
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    combine like terms ... that's all.

    then integrate.
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  5. #5
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    oh ok thanks again!

    so simplified it would just be -x^2+8+2x

    would area=28?
    Last edited by mr fantastic; April 13th 2009 at 08:47 PM. Reason: Merged posts
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  6. #6
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    Quote Originally Posted by Jim Marnell View Post
    oh ok thanks again!

    so simplified it would just be -x^2+8 {\color{red}+} 2x Mr F says: No. Please take greater care with your algebra. The red plus is wrong.

    would area=28? Mr F says: Given the above mistake, I assume 28 will also be wrong.
    The first thing you should have done in this whole question is draw a diagram. Did you do that?
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  7. #7
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    that plus error was my fault, i had it right on paper but typed it in wrong. But yes i had to draw the diagram to go along with the problem but i did it after i completed the problem but definitely would have helped if i drew it before i did the problem
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