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Thread: is this a "geometric formula" or calculus usage?

  1. #1
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    is this a "geometric formula" or calculus usage?

    use a geometric formula to evaluate the integral

    integral from 0 to 3

    $\displaystyle (2x+1)dx$

    I integrated the problem, getting $\displaystyle x^2 + x$

    Then I used the fundamental theorem of calculus, and I got 12-0 = 12..

    Did I use a geometric formula or just calculus?? If I used Calculus, how do I find the answer via geometric formula??
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by elpermic View Post
    use a geometric formula to evaluate the integral

    integral from 0 to 3

    $\displaystyle (2x+1)dx$

    I integrated the problem, getting $\displaystyle x^2 + x$

    Then I used the fundamental theorem of calculus, and I got 12-0 = 12..

    Did I use a geometric formula or just calculus?? If I used Calculus, how do I find the answer via geometric formula??
    The function $\displaystyle f(x)=2x+1$ on the interval $\displaystyle [0,3]$ forms a triangle. Use that.
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  3. #3
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    Ok, I did that.. Got $\displaystyle A = {{1/2}}(3)(7) = {{21/2}}$

    What am I doing wrong??
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by elpermic View Post
    Ok, I did that.. Got $\displaystyle A = {{1/2}}(3)(7) = {{21/2}}$

    What am I doing wrong??
    $\displaystyle f(0)\ne{0}$
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  5. #5
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    I got it now..

    From [0, 3] it isn't a triangle, it's a trapezoid.
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