Let f(r, y) = 2r2 + 2y? - 1. R2 R Rs RA 1. Calculate ff f(r, y)dA by first integrating y and then a, where the regions are: (n) R= R: between z-axis, a = 1, and y= 2r. (b) R= R2: between y-axis, y 1, and y= Ra: between r-axis, r=-1, and y 2x. (c) R (d) R- R: between y-axis, y -1, and y-r.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Problem 1
Let f(x, y) = 21? + 2y? – 1.
%3D
R2
R
2
R3
RA
1. Calculate Jf f(r, y)dA by first integrating y and then a, where the regions are:
(a) R= R: between r-axis, a 1, and y= 2r.
%3D
(b) R= R2: between y-axis, y = 1, and y = -.
(c) R= R3: between z-axis, a = -1, and y 2r.
(d) R R: between y-axis, y= -1, and y -r.
2. Calculate ff f(x, y)dA by first integrating a and then y with the same four regions
in part 1, respectively. I.e.,
(a) R= R: between r-axis, r= 1, and y 2r.
%3D
(b) R= R2: between y-axis, y = 1, and y =
%3D
(c) R= R3: between r-axis, r = -1, and y = 2.r.
%3D
(d) R= R: between y-axis, y = -1, and y =
-u.
3. Verify your solutions by comparing the results from the same regions using different
orders.
Transcribed Image Text:Problem 1 Let f(x, y) = 21? + 2y? – 1. %3D R2 R 2 R3 RA 1. Calculate Jf f(r, y)dA by first integrating y and then a, where the regions are: (a) R= R: between r-axis, a 1, and y= 2r. %3D (b) R= R2: between y-axis, y = 1, and y = -. (c) R= R3: between z-axis, a = -1, and y 2r. (d) R R: between y-axis, y= -1, and y -r. 2. Calculate ff f(x, y)dA by first integrating a and then y with the same four regions in part 1, respectively. I.e., (a) R= R: between r-axis, r= 1, and y 2r. %3D (b) R= R2: between y-axis, y = 1, and y = %3D (c) R= R3: between r-axis, r = -1, and y = 2.r. %3D (d) R= R: between y-axis, y = -1, and y = -u. 3. Verify your solutions by comparing the results from the same regions using different orders.
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