Q3. (a) Evaluate ay dA, where D is the region in R2 bounded by y = sin(x) and y = cos(x) shown in the figure below. 2 1 D 2 3 -1 4.
Q3. (a) Evaluate ay dA, where D is the region in R2 bounded by y = sin(x) and y = cos(x) shown in the figure below. 2 1 D 2 3 -1 4.
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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Question
![Q3. (a) Evaluate
xy dA, where D is the region in R? bounded by y = sin(x) and y = cos(x)
shown in the figure below.
1
1
3
4
-1
-2
(b) Your friend attempted part (a) and obtained a negative value. "That doesn't make
", your friend says. "The double integral should represent the volume under the
surface, so my answer should not be negative!" [continued on next page]
sense",
'In mathematical terminology, a "ball" of radius R is the solid region that lies inside a sphere of radius R. This
is similar to how a "disc" of radius R is the region that lies inside a circle of radius R.
You try to understand your friend's result using the following Geogebra applet. This
applet plots the function f(x, y) = xy in purple and the region D in pink. Using this
applet and your knowledge of integration, explain why your friend's answer is reasonable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc62bdeb3-ddfb-4b0f-a88a-41d3e9d56694%2Fb93497f8-5caf-41f3-a963-9a135d3efcbe%2F2tuklcv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q3. (a) Evaluate
xy dA, where D is the region in R? bounded by y = sin(x) and y = cos(x)
shown in the figure below.
1
1
3
4
-1
-2
(b) Your friend attempted part (a) and obtained a negative value. "That doesn't make
", your friend says. "The double integral should represent the volume under the
surface, so my answer should not be negative!" [continued on next page]
sense",
'In mathematical terminology, a "ball" of radius R is the solid region that lies inside a sphere of radius R. This
is similar to how a "disc" of radius R is the region that lies inside a circle of radius R.
You try to understand your friend's result using the following Geogebra applet. This
applet plots the function f(x, y) = xy in purple and the region D in pink. Using this
applet and your knowledge of integration, explain why your friend's answer is reasonable.
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