Areas and Approximations

In This Chapter

  • Using plane geometry to approximate the area under a curve
  • Computing the true area under a curve
  • Average value of a function
  • Computing the true area between curves
  • Approximate the area under a curve with parabolic arcs

As you read in Chapter 3, the area under a curve can have meaningful applications. While the problems in Chapter 3 consisted of functions that were linear in nature—or composed of line segments—it is also important to be able to compute the area under curved boundaries.

Riemann Sums

We know that the area of a rectangle is equal to the product of length and width, and in this context, ...

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