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Math Help - Finding the area of region between two graphs

  1. #1
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    Finding the area of region between two graphs

    Having trouble doint this problem

    Consider the functions f(x)=x^2-19x+100 and g(x)=-x^2+19x+30. Find the area of the region between the two graphs.

    Any help would be appreciated.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Nasty, but possible.

    Quote Originally Posted by Sundevils View Post
    Consider the functions f(x)=x^2-19x+100 and g(x)=-x^2+19x+30. Find the area of the region between the two graphs.
    Let's find where these curves intersect:

    f(x)=g(x)\implies x^2-19x+35=0.

    So we need to integrate a certain function on the interval \left[ {\frac{{19 - \sqrt {221} }}<br />
{2},\frac{{19 + \sqrt {221} }}<br />
{2}} \right]. The thing is, that in such interval f(x)<g(x), then the integral to compute is

    \int_b^a {\left( {38x - 2x^2 - 70} \right)\,dx},

    where \left[ {a,b} \right] = \left[ {\frac{{19 + \sqrt {221} }}<br />
{2},\frac{{19 - \sqrt {221} }}<br />
{2}} \right].
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by Krizalid View Post
    Nasty, but possible.


    Let's find where these curves intersect:

    f(x)=g(x)\implies x^2-19x+35=0.

    So we need to integrate a certain function on the interval \left[ {\frac{{19 - \sqrt {221} }}<br />
{2},\frac{{19 + \sqrt {221} }}<br />
{2}} \right]. The thing is, that in such interval f(x)<g(x), then the integral to compute is

    \int_b^a {\left( {38x - 2x^2 - 70} \right)\,dx},

    where \left[ {a,b} \right] = \left[ {\frac{{19 + \sqrt {221} }}<br />
{2},\frac{{19 - \sqrt {221} }}<br />
{2}} \right].
    I did the problem the same, but I had a different interval. Can you explain this part:

    f(x)=g(x)\implies x^2-19x+35=0.
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  4. #4
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by angel.white View Post
    I did the problem the same, but I had a different interval. Can you explain this part:

    f(x)=g(x)\implies x^2-19x+35=0.
    Find the points where f(x) = g(x)
    x^2-19x+100 =-x^2+19x+30
    2x^2-38x+70 = 0
    x^2-19x+35 = 0
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  5. #5
    Super Member angel.white's Avatar
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    Quote Originally Posted by colby2152 View Post
    Find the points where f(x) = g(x)
    x^2-19x+100 =-x^2+19x+30
    2x^2-38x+70 = 0
    x^2-19x+35 = 0
    Oh, I did come out with the same answer, I just didn't simplify it as much, so it appeared different
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