Section 5.3: The definite integral and the Fundamental Theorem of Calculus

1. Express the area under a curve as the limit of sum.
2. Define the definite integral as the limit of an appropriate sum and study its properties.
3. Apply the fundamental theorem of calculus to evaluate definite integrals.
4. Use the fundamental theorem of calculus to solve applied problems involving net change.
5. Evaluate definite integrals using the substitution rule.

Annotated slides for Section 5.3.

• Math_1231_slides_5_3_notes.pdf

Please watch the following videos with the prerecorded content for Section 5.3.

1. Motivation for and definition of definite integral
2. Geometric interpretation of definite integral
3. Fundamental Theorem of Calculus
4. Properties of the definite integral
5. Substitution rule for definite integrals
6. Net change Theorem