Unit+2

=Unit 2 (Applications of Integration) -- Chapter 7 (mostly)=


 * ** Blank Unit 2 Notes **
 * ** Unit 2 Exam Review (with answers) **

**Collected Homework by Book Section --** //** UPDATED 3/11/12 **//
 * **7.1**: 7, 13, 15, 17, 19, 21, 23, 27, 29, 33, 37, 39, 43, 49, 53, 57, 59, 63, 65, 75, 81, 85 (//**22 problems**//)
 * **5.4**: 45, 49, 69, 71, 109 (**//5 problems//**)
 * **7.2**: 1, 7, 13, 15, 17, 19, 21, 23, 25, 27, 31, 35, 37, 39, 47, 49, 53, 55, 59, 61, 63, 67 (//**22 problems**//)
 * **7.3**: 1, 5, 11, 15, 17, 21, 23, 25, 27, 29, 35, 37, 39, 41, 43, 45, 47, 53 (//**18 problems**//)
 * **7.4**: 1, 3, 9, 11, 15, 17, 23, 25, 27, 29, 31, 35, 37, 39, 43, 51, 53, 55, 57 (//**19 problems**//)
 * **7.5**: 1, 5, 7, 11, 13, 17, 21, 23, 25, 29, 31, 33, 35, 37, 39, 43 (//**16 problems**//)

I will be collecting this book homework at the time of the Exam for Unit 2, and grading at least one problem from each section (unannounced).

**UNIT 2 Homework Forum -- a wide-open Google Doc where students can collaborate, share, and create a useful resource**
**Answers to all odd-numbered questions from our book.**

**Overall Unit Thoughts**
Now that we are rock stars in the world of integration (or, at least, we have a great start at being fluent with integration), we can appreciate the many ways that integration can be applied in the world. From finding the region bounded by two known curves, to calculating the volume of abnormally shaped figures (i.e., things we don't have formulas for already), to finding curve-lengths and surface-areas, to computing work and pressure; the list of amazing application is very large.

**Section 7.1 -- Area of a Region Between Two Curves**

**Thoughts:** Developed during our time in Calculus I, we can expand our understanding of "integration as area" into some useful geometric areas. Specifically, finding the exact area between two known curves.
 * **7.1 Practice Worksheet**
 * **7.1 Take-Home Quiz**

**Section 5.4 -- Average Value of a Function**

**Thoughts:** Springing from the application of the Mean Value Theorem for Integration, this is a handy little gem. We are now able to find the average value (e.g., "height") of any function, whether it is modeling the amount of air in our lungs over time, the size of a company's profits throughout the year, or anything else.
 * **5.4 Practice Worksheet**

**Section 7.2 -- Volume: The Disk Method**

**Thoughts:** Starting with an extension of integration into three dimensions (literally, rotating a two-dimensional shape out of the page), we develop two main methods for finding the volume of a rotated figure with known boundaries.
 * **7.2 Practice Worksheet**
 * **7.2 Quiz**

**Section 7.3 -- Volume: The Shell Method**

**Thoughts:** An extension of 7.2, this section develops another method for computing exact volume.
 * ** 7.3 Quiz **

**Section 7.4 -- Arc Length and Surfaces of Revolution**

**Thoughts:**
 * ** 7.4 Quiz #1 **
 * ** 7.4 Quiz #2 **

**Section 7.5 -- Work**

**Thoughts:**
 * ** 7.5 Practice problems **
 * ** 7.5 Complete Notes **
 * ** 7.5 Quiz **

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