~~META:title=Chapter 4~~ ~~NOTOC~~ \\ ===== Definite Integrals ===== {{youtube>MivL_1A7Lxw}} {{youtube>psKT74jZafs}} \\ //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. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.2_definite_integrals.pdf|Classroom Slides PDF]] ===== Fundamental Theorem of Calculus ===== {{youtube>JOCPlSK5HM0?list=PLeT8NSIxdCnEQCRpvm1L0Xc6xdmpqzrsx}} {{youtube>p24xTtuVe0s?list=PLeT8NSIxdCnEQCRpvm1L0Xc6xdmpqzrsx}} \\ //Section 4.3 in Stewart's Calculus.//\\ [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.3_fundamental_theorem.pdf|Classroom Slides PDF]] ===== Indefinite Integrals ===== {{youtube>z9nW0k5IQZo}} //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. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.4_indefinite_integrals.pdf|Classroom Slides PDF]] \\ ===== Integration with Substitution ===== {{youtube>4sCmHfBNpwM}} //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. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/4.5_substitution.pdf|Classroom Slides PDF]] \\