Unit 5

Intro

  • Integration has a wide variety of applications.
  • The unit starts with using integration to find the area between graphs of functions.
  • From there, we move into 3-D extensions of graphs to find the volume of solids of revolution using Disk and Washer Method.
  • Integration can also be applied to find the average value of a function, analyze the physics of basic rectilinear motion, analyze slope fields, and exponential growth and decay.

Unit 5 Podcast (coming soon)

5.1 Antiderivatives and Graphing

    • Expressed as Functions of x
    • Expressed as Functions of y
    • Area Between Curves that Intersect at More than Two Points

    • Volumes with Cross Sections
      • Squares
      • Rectangles
      • Triangles
      • Semicircles
    • Volume with Disc Method
      • Revolving Around the x- or y-axis
      • Revolving Around Other Axes
    • Volume with Washer Method
      • Revolving Around the x- or y-axis
      • Revolving Around Other Axes

    • Distance Traveled
    • Arc Length of Curves Given by Parametric Equations

5.1.5 Area of a Region Bounded by Two Polar Curves**

5.2 Modeling with Antiderivatives

    • Differential Equations
    • Exponential Models with Differential Equations
    • Accumulation Functions in Applied Contexts

5.2.2 Straight-Line Motion

5.2.3 Logistic Model**

5.2.4 Parametric and Vector-Valued Motion Equations**

5.2.5 Work

5.2.6 Center of Mass