Definite Integrals


Section 4.2 in Stewart's Calculus.

Preclass Learning Objectives:

  • Definite integrals calculate the area under a function over an interval.
  • Riemann Sums.
  • Properties of definite integrals.


The Fundamental Theorem of Calculus


Section 4.3 in Stewart's Calculus.


Indefinite Integrals

Section 4.4 in Stewart's Calculus.

Preclass Learning Objectives:

  • An indefinite integral of a function is its general antiderivative.
  • The definite integral of a rate of change is the net change.


Integration with Substitution

Section 4.5 in Stewart's Calculus.

Preclass Learning Objectives:

  • Substitution is the rule for integration which corresponds to the chain rule for differentiation.
  • Introduction to integrating with substitution.


Area

Section 5.1 in Stewart's Calculus.

Preclass Learning Objectives:

  • Total area between functions f and g is calculated by integrating the absolute value of the difference of f and g.


Volume

Section 5.2/5.3 in Stewart's Calculus.

Preclass Learning Objectives:

  • Formula for calculating volume using cylindrical shells.
  • Differences between the washer and shell methods.


The Average Value of a Function

Section 5.5 in Stewart's Calculus.

Preclass Learning Objectives:

  • Average Value Formula.