Integration and the Area Between Two Curves

The task is to find the shaded area above between the two curvesandwhich intersect at the points I labelled the curves top and bottom. Using this sophisticated notation, the area is

Sometimes it is not quite so obvious what the equation of either the top or bottom curve is.

The graph isWe have to find the area of the region marked A. The top is obviously

W take as bottom the curvethenare the solutions tosoORso soWe have then