~~META:title=Integrals: Flipped Calculus at Binghamton SUNY~~ ~~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]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/integrals/4.2_definite_integrals_tex|Classroom Slides TEX]] \\ ===== The Fundamental Theorem of Calculus ===== \\ //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]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.3_fundamental_theorem_tex|Classroom Slides TEX]] \\ ===== 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]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.4_indefinite_integrals_tex|Classroom Slides TEX]] \\ ===== 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]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/4.5_substitution_tex|Classroom Slides TEX]] \\ ===== Area ===== {{youtube>g5MMts3tcHI}} //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. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.1_area.pdf|Classroom Slides PDF]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.1_area_tex|Classroom Slides TEX]] \\ ===== Volume ===== {{youtube>FMU8PLT_CSg}} //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. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.3_cylindrical_shells.pdf|Classroom Slides PDF]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.3_cylindrical_shells_tex|Classroom Slides TEX]] \\ ===== The Average Value of a Function ===== {{youtube>IIkXga3YMik}} //Section 5.5 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Average Value Formula. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/5.5_average.pdf|Classroom Slides PDF]] [[https://www2.math.binghamton.edu/p/calculus/resources/calculus_flipped_resources/applications/5.5_average_tex|Classroom Slides TEX]] \\