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**