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The region D in the x, y plane defined by the inequalities 0 < x < 4, 4 < y < V32 – xe can be expressed in polar coordinates as the region D* defined by the inequality a

The region D in the x, y plane defined by the inequalities 0 < x < 4, 4 < y < V32 – xe can be expressed in polar coordinates as the region D* defined by the inequality a

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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The region D in the x, y plane defined by the inequalities 0 < x < 4, 4 < y < V32 –x² can be expressed in polar coordinates as the region D* defined by the inequality a < 0< B, f(0) < r < g(0). with 0 < a, ß < 2n (a) Enter the values of a and ß (in that order) into the answer box below, separated with a comma. (b) Replacing the variable 0 by s, enter the function f(s) into the answer box below. (c) Replacing the variable 0 by s, enter the function g(s) into the answer box below. (d) Evaluate the double integral y I = dA +y? by passing to polar coordinates. Enter your answer symbolically, as in these examples Enter your answer as a symbolic function of s, as in these examples Enter your answer as a symbolic function of s, as in these examples ) 8(1 – ) (B) 4(1 – 1) (C) 4(2+ ) (D) 4(1– ) (E) 4(1+ 5) 4 4
Transcribed Image Text:The region D in the x, y plane defined by the inequalities 0 < x < 4, 4 < y < V32 –x² can be expressed in polar coordinates as the region D* defined by the inequality a < 0< B, f(0) < r < g(0). with 0 < a, ß < 2n (a) Enter the values of a and ß (in that order) into the answer box below, separated with a comma. (b) Replacing the variable 0 by s, enter the function f(s) into the answer box below. (c) Replacing the variable 0 by s, enter the function g(s) into the answer box below. (d) Evaluate the double integral y I = dA +y? by passing to polar coordinates. Enter your answer symbolically, as in these examples Enter your answer as a symbolic function of s, as in these examples Enter your answer as a symbolic function of s, as in these examples ) 8(1 – ) (B) 4(1 – 1) (C) 4(2+ ) (D) 4(1– ) (E) 4(1+ 5) 4 4
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