Applications of Integration: Area between 2 curves: 1 parabola along x, 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 and the upper limit is x=4. Consequently, our integral is

 , or
, or
, or