Change of variables determined by the region Let R be the regionin the first quadrant bounded by the parabolas x = y2, x = y2 - 4, x = 9 - y2, and x = 16 - y2 (see image). Evaluate ∫∫R y2 dA. x = 16 – y?(v = 16)4x = y? – 4(u = -4)3Rx = 9 - v2(v = 9)x= y?(u = 0)+8246u =x- y?v =x + y?X = (u + v)/2y = V(v – u/2v1612Figure 16.822.

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Answered: x = 16 – y? (v = 16) 4 x = y? – 4 (u =…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Change of variables determined by the region Let R be the region
in the first quadrant bounded by the parabolas x = y², x = y² - 4, x = 9 - y², and x = 16 - y² (see image). Evaluate ∫∫_R y² dA.

x = 16 – y?
(v = 16)
4
x = y? – 4
(u = -4)
3
R
x = 9 - v2
(v = 9)
x= y?
(u = 0)
+
8
2
4
6
u =x- y?
v =x + y?
X = (u + v)/2
y = V(v – u/2
v
16
12
Figure 16.82
2.

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