Applications of Integration: Area between 2 curves: 1 quadratic, 1 linear: Find the area, A, bounded by
,
, and
.
First draw a diagram. When you are finished, compare your diagram to this diagram.

We can get the area by using integration to sum up the differential rectangles shown in the diagram. We will need to describe the y-coordinates of the top and bottom ends of each rectangle and the limits of integration. Since the rectangles touch the two curves, we have
, and
.
The lower limit of integration is x = 1. The upper limit is the x-coordinate of the intersection of the curves. At the intersection, each equation yields the same y-coordinate, so we have

, or
, or or, or .
The value 4 is the applicable value for us, and is the upper limit of the integration. Pulling these results together, we get
 , or
, or

, or