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Math Help - Quick integral question

  1. #1
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    Quick integral question

    Does the integral \int^3_0(x^2-1)dx represent the total area bounded by f ( x ) = x^2 - 1 and the x-axis , between x = 0 and x = 3? or is the area larger?
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by wren17 View Post
    Does the integral \int^3_0(x^2-1)dx represent the total area bounded by f ( x ) = x^2 - 1 and the x-axis , between x = 0 and x = 3? or is the area larger?
    Well I will give you a hint...the area between the x-axis and your two curves is given by


    A_{region}=\int_0^{3}{\color{red}{{\bigg|}}}x^2-1{\color{red}{{\bigg|}}}{dx}
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  3. #3
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    I think i figured out that the area is 6 but im not sure if its larger or not
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by wren17 View Post
    I think i figured out that the area is 6 but im not sure if its larger or not
    x^2-1=0\Rightarrow{x=\pm{1}}

    1 being the only relevant result since -1 is outside of our domain

    \therefore\int_0^{3}|x^2-1|dx=\int_1^{3}x^2-1dx-\int_0^{1}x^2-1dx=\frac{22}{3}\approx{7.3333}

    Now

    \int_0^{3}x^2-1dx=\bigg[\frac{x^3}{3}-x\bigg]\bigg|_{x=0}^{3}=6

    So now what can you conclude?
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