7.1 The Area Under a Curve

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

• 1. The Area Under a Curve [University of British Columbia]

  2. Read about the area of a triangle under a line, the area under a parabola, and the summary at the end. Skip the section on the area under an exponential.

  3. Area Problem [Paul's Online Math Notes]

  4. Riemann Sums [IntegralCALC]

  5. After reading about the Riemann sums for approximating the area between the curve and the x-axis, view two videos that are available at the top of the page, one on using the right endpoint method for f(x)=2 - x2 and the other on using the midpoint method for

  6. .

  7. Approximation of Areas [University of Tennessee]

  8. Note: This site requires either Java or Flash for some parts.

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

• 1. Area Problem [Paul's Online Math Notes]

  2. The area under a curve (from University of New England). Watch the video and do the practice problems. Skip problems #3 and 4. Answer and explanation are available for each problem.

Additional Resources

Below are additional resources that help reinforce the content for this module.

• 1. The Area under a Curve [University of Houston] (approximation of areas with sums of rectangle areas. Right-endpoint, left-endpoint, and midpoint approximations; upper and lower sum.)

  2. YouTube video: Introduction to Area Under a Curve