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Thread: area between curves

  1. #1
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    area between curves

    find the area enclosed by the curves y= x^2 + 7 and y= 2x^2 +3

    thanks
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Equate the functionsto find the limits of integration.

    Then we get:

    $\displaystyle \int_{-2}^{2}\left[(x^{2}+7)-(2x^{2}+3)\right]dx$
    Last edited by galactus; Nov 24th 2008 at 05:38 AM.
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Let $\displaystyle f(x)=x^2+7$ & $\displaystyle h(x)=2x^2+3.$

    These curves intersect at $\displaystyle f(x)=h(x),$ this yields $\displaystyle [-2,2].$ We need to integrate a certain function in such interval. We have $\displaystyle f(x)\ge h(x),$ and so our integral is

    $\displaystyle \int_{ - 2}^2 {\left\{ {\left( {x^2 + 7} \right) - \left( {2x^2 + 3} \right)} \right\}\,dx} ,$ which confirms galactus' result.

    (Exploiting the symmetry saves time on calculations.)
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