An Aerial View of the Area Problem
In This Chapter
Measuring the area of shapes by using classical and analytic geometry
Understanding integration as a solution to the area problem
Building a formula for calculating definite integrals using Riemann sums
Applying integration to the real world
Considering sequences and series
Looking ahead at some advanced math
Humans have been measuring the area of shapes for thousands of years. One practical use for this skill is measuring the area of a parcel of land. Measuring the area of a square or a rectangle is simple, so land tends to get divided into these shapes.
Discovering the area of a triangle, circle, or polygon is also easy, but as shapes get more unusual, measuring them gets harder. Although the Greeks were familiar with the conic sections — parabolas, ellipses, and hyperbolas — they couldn’t reliably measure shapes with edges ...