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5. (a) Let D be the region located in the first quadrant of R? between the two circles of radii 1 and 2 centered on the origin. Evaluate ry drdy . 1+ (r2 + y²)² ´ (b) Consider the thin disk centered on the origin in R? of radius 1. Suppose it is made of a material with mass density function p(x, y) = log (4(1 +x* + y®)) in grams per units of area. Show that the mass of the disk exceeds 27 log 2 grams.

5. (a) Let D be the region located in the first quadrant of R? between the two circles of radii 1 and 2 centered on the origin. Evaluate ry drdy . 1+ (r2 + y²)² ´ (b) Consider the thin disk centered on the origin in R? of radius 1. Suppose it is made of a material with mass density function p(x, y) = log (4(1 +x* + y®)) in grams per units of area. Show that the mass of the disk exceeds 27 log 2 grams.

Advanced Engineering Mathematics
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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5. (a) Let D be the region located in the first quadrant of R? between the two circles of radii 1 and 2 centered on the origin. Evaluate ry dzdy . 1+ (r2 + y²)² ´ (b) Consider the thin disk centered on the origin in R? of radius 1. Suppose it is made of a material with mass density function p(x, y) = log (4(1 +x* + y®)) in grams per units of area. Show that the mass of the disk exceeds 2n log 2 grams.
Transcribed Image Text:5. (a) Let D be the region located in the first quadrant of R? between the two circles of radii 1 and 2 centered on the origin. Evaluate ry dzdy . 1+ (r2 + y²)² ´ (b) Consider the thin disk centered on the origin in R? of radius 1. Suppose it is made of a material with mass density function p(x, y) = log (4(1 +x* + y®)) in grams per units of area. Show that the mass of the disk exceeds 2n log 2 grams.
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