Math 175 Week 1 Written Assignment Summer 2015

Instructions:

All problems are due at the beginning of class on Thursday, May 14th. Quality of presentation is a significant part of your grade. This includes:

Neatness. Sloppy work will score poorly, if it gets graded at all.

Organization. Your work must be easy to find and easy to follow.

Communication. Your work must show how you reached your answer, and you mustmake correct use of mathematical notation.

Pay attention to specific answer formatting requirements in each individual problem.

Some problems will have the instruction Write an integral for... In these problems youDO NOT compute your integral. Your final answer should look like number

number

formula

and your formula must be correctly expressed in terms of the variable of integration.

Print the next two pages of this assignment. The first two problems are to be done on your print out. The last problem must be done on your own paper.

Problems:

Problems begin on the next page. Print out the next two pages.

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1. (5 points) The region below is bounded by y = cos(pix) and y = 1. Suppose you want to findits area by integrating along the x-axis.

(a) Draw a typical rectangle for this slicing strategy.

(b) Correctly label the dimensions of your slice.

(c) Find the area of your slice.

(d) Write an integral for the shaded area, expressed in terms of x.

Do not evaluate the integral.

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2. (5 points) Repeat problem 1, for the region bounded by y = cos(pix) and y = 1. But this timeintegrate along the y-axis.

(a) Draw a typical rectangle for this slicing strategy.

(b) Correctly label the dimensions of your slice.

(c) Find the area of your slice.

(d) Write an integral for the shaded area, expressed in terms of y.

Do not evaluate the integral.

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3. (10 points) Suppose a thin plate is in the shape of the region bounded by the curves x+y2 = 4and y x = 2, where x and y are measured in meters. Also this plate has a mass density of60 grams per meter2.

Find the mass of this plate. Show all work. At a minimum, this means:

Write your solution on a separate sheet of paper. Create a properly labeled graph of this region on graph paper. Quality counts! State which slicing strategy you used. This means state your axis of integration. Draw and label a typical rectangle for your slicing strategy. If your slicing strategy requires you to break into more than one region, then you must

draw and label a typical rectangle in each region.

Show or explain how you found the bounds of integration. Write an integral (or a sum of integrals) for the region. Either show work or explain how you computed your integral(s). Answer the question asked with proper units. You are welcome to use a calculator to solve equations or calculate integrals. If you do

so, you must state how you used your calculator.

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