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Math Help - Area between two curves (simple question)

  1. #1
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    Area between two curves (simple question)

    Hi,

    I'm trying to find the area between the curves:

    y=x^2 + 4x +1 and
    y = 3x+3

    A sketch shows me that y =3x+3 is above y=x^2 +4x +1 and I have found the intersection points are x=-2 and x=1.

    Does this then mean that I just need to evaluate the integral of (3x+3)-(x^2+4x+1) from -2 to 1?

    I know that some of this area lies underneath the x-axis and not sure if I need to be accounting for that or not.

    Thanks!
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  2. #2
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    Re: Area between two curves (simple question)

    Hi Andy, you don't have to worry if one of the graphs is below the x-axis. In fact, both graphs can be below the x axis and the definite integral ∫ [higher function] - [lower function] dx = area between the curves still holds. So you're right, just evaluate the integral you said before.
    Thanks from andy000
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  3. #3
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    Re: Area between two curves (simple question)

    Thanks very much
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