Topic 2 – Approximate Integrals with Error Estimation

• • Review of Approximate Integrals – The Main Idea
  • Trapezoidal and Midpoint Rule Errors
  • Area Given Data Points Example – Trapezoidal and Simpson’s Rules

Topic 3 – Review of Indeterminate Forms and L’Hopital’s Rule

• • L’Hopital’s Rule – The Main Idea
  • Indeterminate Forms – The Main Idea
  • Logarithmic Techniques and L’Hopital’s Rule
  • Using L’Hospital’s Rule with Logs
  • Using L’Hospital’s Rule with Trig Functions
  • Another Example Using L’H Rule with Trig Expressions

Topic 4 – Improper Integrals

• • Improper Integrals – The Main Idea
  • Improper Integral with Infinite Limits of Integration
  • Improper Integral – Ex. 3
  • Improper Integral with Discontinuity in [a, b]
  • Improper Integral with Trig Functions
  • Evaluating an Improper Integral

Topic 5 – Arc Length

• • Arc Length – The Main Idea
  • Arc Length – Two Examples
  • Arc Length and FTC

Topic 6 – Area of a Surface of Revolution

• • Surfaces of Revolution – The Main Idea
  • Area of a Surface of Revolution Example 1
  • Area of a Surface of Revolution Example 2

Topic 7 -Applications to Physics and Engineering

• • Hydrostatic Pressure and Fluid Force
  • Fluid Force – Porthole Example
  • Fluid Force – Trapezoidal Trough Example
  • Moment and Centers of Mass – The Main Idea
  • Centroid of Region Example