Topic 0 – Integration by Substitution (Review)

• • Integration with u-substitution and e^x
  • Integrating a trig expression using u-substitution
  • Integrating a trig expression using a power-reducing formula

Topic 1 – Volume of Solids of Revolution – The Disk Method

• • Volumes – The Main Idea
  • Revolving a Region about Different Axes
  • Volume of a Solid Formed by Two Regions
  • Volume of a Spherical Bead

Topic 2 – Volume of Solids of Revolution – The Shell Method

• • Volumes using the Shell Method – The Main Idea
  • Volumes using the Shell Method – Ex. 2
  • The Disk Method vs. The Shell Method
  • Revolving a Region about Three Different Axes

Topic 3 – Work

• • Pumping Water – Cylindrical Tank
  • Pumping Water – Spherical Tank
  • Pumping Oil – Tank formed by Revolved Region

Topic 4 – Integration by Parts

• • Integration by Parts Example with an Exponential Function
  • Integration by Parts Example with a Log
  • Integrating a trig expression using integration by parts

Topic 5 – Trig Integrals

• • Trig Integrals – The Main Idea
  • Trig Integral with Tangent and Secant
  • Circular Trig Integral
  • Trig Integral with Cosecant and Cotangent

Topic 6 – Integrating using Trig Substitution

• • Trig Substitution – The Main Idea
  • Trig Substitution – Ex. 2
  • Trig Substitution – Ex. 3
  • Trig Substitution – Ex. 4
  • Definite Integral Example
  • Double Substitution Example

Topic 7 – Integration of Rational Functions using Partial Fractions

• • Integration using Partial Fraction Decomposition – The Main Idea
  • Integration using Partial Fraction Decomposition – Ex. 2
  • Integration using Partial Fraction Decomposition – Ex. 3
  • Integration using Partial Fraction Decomposition – Ex. 4
  • Integrating by Splitting the Fraction