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calculus:resources:calculus_flipped_resources:integrals

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.