Math 31 – Unit #8 The Antiderivative and Integrals
Unit 8 discusses how to find the antiderivatives of all types of functions. This is the opposite process of derivatives and can be used to solve problems in physics, geometry and more. This process is the way many physics formulas have been developed.
Each section below will have several instructional videos for each part, including examples and their solutions. After all parts are completed within a section, there will be a set of questions to be done and handed in. After all sections are completed, there will be a single summative assessment (unit exam) covering all material from this unit.
Unit Sections
a) Introduction to Antiderivatives/Integrals i. Basic Indefinite Integrals ⇒ Teaching Video with Embedded Questions ii. Integrals Involving Trig and Logs ⇒ Teaching Video with Embedded Questions iii. Solving Differential Equations ⇒ Teaching Video with Embedded Questions iv. Taking integrals of Multiple Functions (Reverse Chain Rule) ⇒ Teaching Video with Embedded Questions
There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After the subsection is done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walkthrough solutions video will then be given to the students to self assess their work. Upon completion of the formative assessments, there will be a summative assessment for the entire section.
b) Antiderivatives as an Area i. Area Under a Curve ⇒ Teaching Video with Embedded Questions ii. Area Between two Curves ⇒ Teaching Video with Embedded Questions There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After the subsection is done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walkthrough solutions video will then be given to the students to self assess their work. Upon completion of the formative assessment - please continue to the next section.
c) Definate Integrals and Applications i. Fundamental Theorem of Calculus ⇒ Teaching Video with Embedded Questions There will be example questions within each video which students will be asked to do and then they will be walked through the solutions together. After the subsection is done there will be a SINGLE FORMATIVE ASSESSMENT that students will complete and then submit. A walkthrough solutions video will then be given to the students to self assess their work. Upon completion of the formative assessment, there will be a summative assessment for both section b and c.
d)ANTIDERIVATIVES/INTEGRALS FINAL SUMMATIVE ASSESSMENT
The Integrals/Antiderivatives Unit will have 3 summative assessments. Three smaller assignments and 1 unit exam. These assessments will represent the entire grade for the Integrals/Antiderivatives unit of the Math 31 course.
Once a student reaches the point in the Unit where the summative assessments are posted, they should be completed before the next sections are attempted.
Once all formative and minor summative assessments are completed, students will write the unit Summative assessment at a supervised site.
Students will have the opportunity to rewrite this Summative Assessment at any time BUT through instructor consultation and guidance, students will have to demonstrate evidence of new learning and preparedness.