: The region D in the x, y plane defined by the inequalities 0 ≤ y ≤4, √√4y-1² ≤x≤ Isas √√16-₁², can be expressed in polar coordinates as the region D* defined by the inequality a ≤ 0≤ß, f(0) ≤ r ≤ g(0), with 0 ≤ a, ß < 2π. (a) Enter the values of a and ß, separated by a comma, in that order. (b) Replacing the variable by s, enter the function f(s). (c) Replacing the variable by s, enter the function g(s). (d) Evaluate the iterated integral √16-1² TO THE (A)-+6 2x+3 by passing to polar coordinates. dx dy 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 +6ñ (B) 20+12µ (C) −¹²+18ë (D) −²º +6ñ (E) 4 – 6ñ
: The region D in the x, y plane defined by the inequalities 0 ≤ y ≤4, √√4y-1² ≤x≤ Isas √√16-₁², can be expressed in polar coordinates as the region D* defined by the inequality a ≤ 0≤ß, f(0) ≤ r ≤ g(0), with 0 ≤ a, ß < 2π. (a) Enter the values of a and ß, separated by a comma, in that order. (b) Replacing the variable by s, enter the function f(s). (c) Replacing the variable by s, enter the function g(s). (d) Evaluate the iterated integral √16-1² TO THE (A)-+6 2x+3 by passing to polar coordinates. dx dy 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 +6ñ (B) 20+12µ (C) −¹²+18ë (D) −²º +6ñ (E) 4 – 6ñ
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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Transcribed Image Text:7: The region D in the x, y plane defined by the inequalities
0 ≤ y ≤ 4, √√4y-y² ≤ x ≤ √16-₁²,
a):
b):
c):
can be expressed in polar coordinates as the region D* defined by the inequality
a ≤ 0 ≤ ß, f(0) ≤ r ≤ g(0),
with 0 ≤ a, ß < 2π.
(a) Enter the values of a and ß, separated by a comma, in that order.
(b) Replacing the variable by s, enter the function f(s).
(c) Replacing the variable by s, enter the function g(s).
(d) Evaluate the iterated integral
I=
=
St. S.
16-
2x + 3
by passing to polar coordinates.
(A) -+
#7(d): Select Part (d) choices.
dx dy
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
+6π (B) 20+12µ (C) − +187 (D)
-
+6π (E) 4-6π
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