MA101: Single-Variable Calculus I

8.7: Physical Applications

• We will now apply what we have learned about integration to various aspects of science. You may know that in physics, we calculate work by multiplying the force of the work by the distance over which it is exerted. You may also know that density is related to mass and volume. But we now know that distance and volume are very much related to integration. In this subunit, we will explore these and other connections.
  

• 8.7.1: Distance

  • Whitman College: David Guichard's "Calculus, Chapter 9: Applications of Integration, Section 9.2: Distance, Velocity, Acceleration" URL

    Read Section 9.2 (pages 192-194).
    

  • Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Displacement vs. Distance Traveled" URL

    Work through each of the three examples on the page. As in any assignment, solve the problem on your own first. Solutions are given beneath each example.
    

• 8.7.2: Mass and Density

  • University of Wisconsin: H. Jerome Keisler's "Elementary Calculus, Chapter 6: Applications of the Integral, Section 6.6: Some Applications to Physics" URL

    Read this section (pages 341-351).
    

• 8.7.3: Moments

  • Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Moments and Centers of Mass" URL

    Work through each of the four examples on the page. As in any assignment, solve the problem on your own first. Solutions are given beneath each example.
    

• 8.7.4: Work

  • Whitman College: David Guichard's "Calculus, Chapter 9: Applications of Integration, Section 9.5: Work" URL

    Read Section 9.5 (pages 205 through 208). Work is a fundamental concept from physics roughly corresponding to the distance traveled by an object multiplied by the force required to move it that distance.
    

  • Clinton Community College: Elizabeth Wood's "Supplemental Notes for Calculus I: Work, Fluid Pressures, and Forces" URL

    Work through each of the seven examples on the page. As in any assignment, solve the problem on your own first. Solutions are given beneath each example.