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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- Dec 3rd 2007, 12:18 PMSundevilsFinding 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. - Dec 3rd 2007, 12:58 PMKrizalid
Nasty, but possible.

Let's find where these curves intersect:

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

So we need to integrate a certain function on the interval $\displaystyle \left[ {\frac{{19 - \sqrt {221} }}

{2},\frac{{19 + \sqrt {221} }}

{2}} \right].$ The thing is, that in such interval $\displaystyle f(x)<g(x),$ then the integral to compute is

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

where $\displaystyle \left[ {a,b} \right] = \left[ {\frac{{19 + \sqrt {221} }}

{2},\frac{{19 - \sqrt {221} }}

{2}} \right].$ - Dec 3rd 2007, 02:06 PMangel.white
- Dec 3rd 2007, 02:45 PMcolby2152
- Dec 3rd 2007, 05:27 PMangel.white