Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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. Y 1 D 3 4 -1 -2 (b) Your friend attempted part (a) and obtained a negative value. "That doesn't make sense", your friend says. "The double integral should represent the volume under the surface, so my answer should not be negative!" [continued on next page] '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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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. Y 1 D 3 4 -1 -2 (b) Your friend attempted part (a) and obtained a negative value. "That doesn't make sense", your friend says. "The double integral should represent the volume under the surface, so my answer should not be negative!" [continued on next page] '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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