"Find the area contained between the curves y=x^2-6x+4 and x+y=0"
My question is: Is there a way to tell which graph is the outer/top curve and which would be the inner/lower curve without having to draw a graph?
$\displaystyle y = x^2 - 6x + 4$ and $\displaystyle x+y = 0$ intersect when $\displaystyle x + x^2 - 6x + 4 = x^2 -5x+4 = (x-1)(x-4)=0$. So whichever has the higher value of $\displaystyle y$ at $\displaystyle x=2$, for example is the top curve.