# Calculus (AP Math BC) Spring 2018

### Calculus Homework

Homework Sources:

Napkin Ring on Amazon

Next Calculus Test: Wed January 24, 2018 (generally every other Wednesday)

Due Date Assignment
Mon 1/8
WeBWork: Winter-Break-2017-2018

Tue 1/9
* Reconsider two cylinders each with a radius of $$R$$ intersecting at right angles as shown in this diagram. Last semester your volume elements were “rectanglular disks” (squares) to find the the volume of the intersecting region. This time your method is to use “rectangular shells” as volume elements

* TurnIn: A typed second draft of your solution as a complete Four Section Write-up. See Sample write-up. Be sure to comment on the method and why your answer is reasonable.

* (Optional: You might want to review volume by shells by actively watching MIT Volume of revolution via shells.)

Wed 1/10
* WeBWork Volume_Practice_1
Note: Problem 4 is multiple choice, and you only get two tries to get the correct answer(s)
* Finish the Ladder problem from Kwiki 20055

* Start a journal. Each day spend a few minutes summarizing the concepts we worked on in class and in the homework. You might use the journal to ask yourself questions on concepts. For example,
When finding volumes of revolution when is it better to use shells than to use washers?

Thu 1/11
* Carefully read HWS Integration by Parts Introduction
* Use Integration by Parts on $\int x e^{-x} \, dx$ Be sure to check your answer.
* In your journal write-up a solution to question 4 (Battle of the Limits) on Kwiki 20057

Fri 1/12
* Determining $$u$$ and $$dv$$ takes some practice. Actively watch MIT Integration by parts 1
* Finish Kwiki 20058 — (but don’t look up answers and/or solutions)

* Journals:
1. Transfer your journal from your computer to the new book. Now that you have an empty journal book, bring it up to date by printing your computer entries (or writing new ones) for Monday, Tuesday, and Wednesday, and pasting them into the pages of the book. Each day’s entry should have be on a new page with the day and date in the upper right hand corner. Please only use the front side of each sheet of paper. With 168 sheets you will not run out of paper.
2. Today’s entry: You are welcome to use your computer and paste your entries in the notebook, write into the notebook, and do both. At a minimum, today’s entry must include how to show that the product rule leads to the formula for integration by parts.

Tue 1/16
* WeBWorK bic_spring_misc_01
— Note: Only two tries on the matching question.

* TurnIn: A 3rd Draft of Intersecting Cylinder Volume by “rectangular shells”
Focus on improving your explanation of how you develop your volume element. A couple of people in Block 5 annotated this diagram to show a typical rectangular box. You can do this by printing a copy of the diaygram and using a pencil and straight-edge…

* Remember, your journal should include a dated entry after each class on a new page. Today’s Kwiki should be a good starting point.

Wed 1/17
* Be prepared (as a group) to present any of the volume problems from today’s Kwiki on the board.
In addition to the setups, evaluate the integrals.

Thu 1/18 * Work on Particle, the dog (see question 6 of the Kwiki 20061).
* TurnIn: A brief second draft of a write-up of your game plan and solution sections for part (a) of the Particle, the dog question
— Find an equation for a function, $$P(x)$$ that takes the owner’s $$x$$ value and produces the distance Particle has traveled along the sine curve since starting at the origin. Be sure to explain how you developed $$dP$$, a distance element.
Hint: You will ultimately need to use a calulator to get values for $$P(x)$$ other than $$P(0)$$.
Note: If you do not have an equation for $$P(x)$$, write a question where the answer to that question would help you get closer to a equation for $$P(x)$$. Explain how the answer would help you.

Fri 1/19
* The distance Particle, the Dog travels along a curve is called arc length.
Compute the length of the curve $y=x^{3/2} \, \, \text{ for } \,\, x \in [0,4]$
* Actively watch MIT arclength

Mon 1/22
* Select two of the questions from Kwiki 20063 that is not on your group’s poster. Write up each question, and enter a second draft into your journal. A neatly handwritten version or pasting in a typed printout is fine.

* Journal Update: The first test is coming on Wednesday. Make an entry that includes an annotated list of topics we have studied in this second semester. Other ideas are always welcome.

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## Kwikis

### Set 1S

• Kwiki 20055 sphere by shells (again), ladder problem
• Kwiki 20056 thinking about $$u$$-substitution, intersecting cylinders “shells”, ladder problem
• Kwiki 20057 thinking about $$\displaystyle \int_0^1 \sqrt{1-x^2} \, dx$$, (First Battle of the Limits)
• Kwiki 20058 integration by parts
• Kwiki 20059 integration by parts, another battle of the limits, still thinking about $$\displaystyle \int_0^1 \sqrt{1-x^2} \, dx$$
• Kwiki 20060 Napkin Ring Problem, misc volume problems
• Kwiki 20061 For group presentations: Napkin Ring Problem, misc volume problems; $$\displaystyle \int \sin^2(x) \, dx$$ using integration by parts, start Particle, the Dog
• Kwiki 20062 $$\displaystyle \int \cos^2(x) \, dx$$ using integration by parts, more Particle, the Dog
• Kwiki 20063 Seven potential poster problems

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