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Evaluate the double integral by first identifying it as the volume of a solid. 120 Je 4 dA, R = {(x, y) | -2 ≤ x ≤ 2, 2 ≤ y ≤7} X

Evaluate the double integral by first identifying it as the volume of a solid. 120 Je 4 dA, R = {(x, y) | -2 ≤ x ≤ 2, 2 ≤ y ≤7} X

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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Evaluate the double integral by first identifying it as the volume of a solid. J[² 120 4 dA, R = {(x, y) | -2 ≤x≤ 2, 2 ≤ y ≤7} x Need Help? Read It Watch It
Transcribed Image Text:Evaluate the double integral by first identifying it as the volume of a solid. J[² 120 4 dA, R = {(x, y) | -2 ≤x≤ 2, 2 ≤ y ≤7} x Need Help? Read It Watch It
Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = x-y p = g(x, y) = 2(x+y) Vf(x, y) = yi+xj Avg = 2^i + 2hj Then 2 = = 2 implies that x = y Therefore, the rectangle with maximum area is a square with side length P 4
Transcribed Image Text:Use Lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. Let the sides of the rectangle be x and y and let f and g represent the area (A) and perimeter (p), respectively. Find the following. A = f(x, y) = x-y p = g(x, y) = 2(x+y) Vf(x, y) = yi+xj Avg = 2^i + 2hj Then 2 = = 2 implies that x = y Therefore, the rectangle with maximum area is a square with side length P 4
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