Unit 5

Prereq Test 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.

Overview 5

Inquiry Activity 5

Key Terms

Unit 5 Podcast (coming soon)

5.1 Antiderivatives and Graphing

5.1.1 Area Between Graphs of Functions

• • Expressed as Functions of x

  • Expressed as Functions of y

  • Area Between Curves that Intersect at More than Two Points

5.1.2 Average Value of a Function

5.1.3 Volumes

• • Volumes with Cross Sections

    • Squares

    • Rectangles

    • Triangles

      • equilateral

      • isosceles

      • right

    • 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

5.1.4 Arc Length (Calculus 2)

• • Distance Traveled

  • Arc Length of Curves Given by Parametric Equations

5.1.5 Area of a Region Bounded by Two Polar Curves (Calculus 2)

5.2 Modeling with Antiderivatives

5.2.1 Modeling

• • Differential Equations

  • Exponential Models with Differential Equations

  • Accumulation Functions in Applied Contexts