I'm taking calculus and we're up to areas between curves. Thing is that unless I do a table of values and graph, or I'm given an easy transformation, its really hard to figure out which graph is the top and bottom so I can do
$A=\int_a^b \! F_{top} - F_{bottom} \, \textrm{d}x$ or $A=\int_c^d \! F_{right} - F_{left} \, \textrm{d}x$
Also, what's a quick way of determining a problem in which I'll have to add two integrals and when I only need to solve one?
There is no quicker way, I think, than graphing the curves as accurately as possible, finding the points of intersection around the area enclosed...and see the limits /extreme point positions for $x,y$.