What This Document Is
This is a problem set, specifically Worksheet 2, from a Calculus II course (MATH 132) at Washington University in St. Louis, from the Fall 2014 semester. It’s designed to be used in a Peer-Led Team Learning (PLTL) session, indicating a focus on collaborative problem-solving. The worksheet centers on core concepts within the second semester of calculus, building upon foundational principles established in Calculus I. Expect a focus on applying integral calculus and related techniques.
Why This Document Matters
This resource is ideal for students currently enrolled in a Calculus II course, or those reviewing key concepts in preparation for further study. It’s particularly beneficial for students who thrive in a collaborative learning environment and want to test their understanding through practice problems. It’s best utilized *during* study sessions, either individually as a challenge or, as intended, within a PLTL group to discuss approaches and solidify comprehension. Students preparing for exams will find it valuable for identifying areas needing further review.
Common Limitations or Challenges
This worksheet does not provide a comprehensive lecture or re-teaching of concepts. It assumes a baseline understanding of integral calculus principles. It also doesn’t offer fully worked-out solutions; the intention is for students to actively engage with the problems and develop their own problem-solving strategies. While it touches on various applications, it won’t cover *every* possible application of the covered techniques. It is a snapshot of practice problems from one specific session.
What This Document Provides
* A series of problems focused on calculating areas between curves using integral calculus.
* Practice applying both the shell method and the washer method to determine volumes of solids of revolution.
* Exercises involving finding the arc length of a curve.
* Problems requiring the calculation of volumes of solids with specific base shapes and cross-sections.
* A problem focused on applying fundamental theorem of calculus to determine a function value.
* Discussion prompts designed to encourage reflection on study habits and exam preparation strategies.