A vase as shown in the figure is to be drawn as a mural with all lengths in feet. The outline will be black and the interior will be blue. To draw the outline, we need to know its total length since the amount of black paint needed will be proportional to it. To color the inside blue, we need to know the area. The two curves are well approximated by x = siny + 2 and x = -siny - 2 for 0 ≤ y ≤ 2. The horizontal segments are at y = 0 and y = 2π. 1. Set up and evaluate an integral for the area of the region. Include units in your answer. 2. Does the computed area seem reasonable? Can you make a geometrical argument resulting in the same answer? 3. Set up an integral for the length of one of the sides of the outline of the vase. Use technology to evaluate this integral. Round to two decimal places and include units in your answer. 4. What is the total length of the outline of vase rounded to two decimal places? Include units.
A vase as shown in the figure is to be drawn as a mural with all lengths in feet. The outline will be black and the interior will be blue. To draw the outline, we need to know its total length since the amount of black paint needed will be proportional to it. To color the inside blue, we need to know the area. The two curves are well approximated by x = siny + 2 and x = -siny - 2 for 0 ≤ y ≤ 2. The horizontal segments are at y = 0 and y = 2π. 1. Set up and evaluate an integral for the area of the region. Include units in your answer. 2. Does the computed area seem reasonable? Can you make a geometrical argument resulting in the same answer? 3. Set up an integral for the length of one of the sides of the outline of the vase. Use technology to evaluate this integral. Round to two decimal places and include units in your answer. 4. What is the total length of the outline of vase rounded to two decimal places? Include units.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A vase as shown in the figure is to be drawn as a mural with all
lengths in feet. The outline will be black and the interior will
be blue. To draw the outline, we need to know
its total length since the amount of black paint needed will be
proportional to it. To color the inside blue, we need to know the
area. The two curves are well approximated by x = siny + 2 and
x = -siny - 2 for 0 ≤ y ≤ 2. The horizontal segments
are at y = 0 and y = 2π.
1. Set up and evaluate an integral for the area of the region.
Include units in your answer.
2. Does the computed area seem reasonable? Can you make a geometrical argument resulting
in the same answer?
3. Set up an integral for the length of one of the sides of the outline of the vase. Use technology
to evaluate this integral. Round to two decimal places and include units in your answer.
4. What is the total length of the outline of vase rounded to two decimal places? Include units.
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