Find the area bounded by f(x)= -x^2+x+3 and g(x)=2x + 1

Question

anonymous · Answer

do you know which one is on top

anonymous · Answer

i believe f(x)= -x^2 + x+3

mathteacher1729 · Answer

Do you know where the functions intersect? 
(are you allowed to use a graphing program to view the functions?)

anonymous · Answer

No. I am not sure where they intersect

mathteacher1729 · Answer

To find where they intersect, set the functions equal to one another: 

In other words, solve 

-x^2+x+3 =2x + 1 

(it's a quadratic which factors nicely). :)

anonymous · Answer

f(x)=g(x)
you will find where they intersect

across · Answer

$$f(x)=-x^2+x+3,$$$$g(x)=2x+1.$$
$$f(x)=g(x),$$$$-x^2+x+3=2x+1,$$$$-x^2-x+2=0\implies(-x+1)(x+2)=0.$$
$$\int_{-2}^{1}\int_{2x+1}^{-x^2+x+3}dydx.$$

anonymous · Answer

is it 4/3 then across?

anonymous · Answer

Mathteacher1729: if i factor it i get 2 and 1.

across · Answer

I got 9/2.

mathteacher1729 · Answer

Wow, across, that is an interesting solution.  :D I'm willing to wager that treyhud's class has not yet covered double integrals though...

Treyhud, what was the factorization you obtained?  (the roots you gave are not quite accurate).

anonymous · Answer

whew again double integrals