1 page math paper

Calculus II

Writing Assignment 1: Infinite area and finite volume 1. Information

• You may work alone, or in groups of two or three. Everyone must participate in all parts of the project.

• Either typed or handwritten. Just make sure it is reasonably readable.

• No restriction on the length, but probably it will be 1-3 pages.

2. Important Remarks

In this assignment, you must explain your conclusion so that any strangers with enough background can understand and agree. In particular,

• sentences must be complete and grammatically correct, • mathematical expressions follow the standard rules, and

• arguments are complete and logical.

You should not expect me to read your intention. For more information about writing in mathematics, refer to the handout given at the beginning of the semester.

3. Warning!

You are allowed to see any resources, including but not limited to, textbooks, the class notes, other books, web sites. However, you should NEVER try to copy something that was written by somebody else. Academic integrity is considered to be very important. It is much more important than how you perform in individual courses. It is advisable that you give the list of references.

(See the next page for the problems)

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Problem 1. Find all values of p have the following property: The area of the region bounded by y = x−p (1 ≤ x < ∞), x = 1, and the x-axis is infinite, but the volume of the solid obtained by rotating the region about the x-axis is finite.

Remark. Without proof, you may use the following formula: The volume of the solid obtained by rotating the region under the curve y = f(x) (a≤x≤b) about the x-axis is

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