Which property of double integrals should be applied as a logical first step to evaluate R (2z-1) (y-3y+1) dA over the region R = {(2,9)|0
Which property of double integrals should be applied as a logical first step to evaluate R (2z-1) (y-3y+1) dA over the region R = {(2,9)|0
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:Question
Which property of double integrals should be applied as a logical first step to evaluate R (27-1) (- 3y+1) dA
over the region R=
{(1,y)0 <<1, 0<y< 2}?
Select the correct answer below:
O If f(z,v) and g(z,y) are integrable over the rectangular region R, then the sum f(z, y) + g(z, y) is integrable and
If f(z, y) is integrable over the rectangular region Rand c is a constant, then cf(z, y) is integrable and
lR cf(z, v)dA= c flR F(z,v)dA.
If f(z, y) is integrable over the rectangular region Rand S and 7 are subregions of R such that R
SnT 0 except an overlap on the boundaries then , Az.v)dA , f(z.v)dA + f, f(z, y)dA.
SUT and
OIf f(z,y) and g(z,y) are integrable over the rectangular region Rend fr.) 2 9(z, y) for (z, y) in R., then
![DCICLL U C LUICLL OIISTCI UCIUW.
O If f(z.v) and g(z, v) are integrable over the rectangular region R, then the sum f(z,v) + g(z,v) is integrable and
ORz.9) + g(z,v)dA = OR f(z,v)dA + ffg9(z,v)dA
Of (z,y) is integrable over the rectangular region Rand c is a constant, then cf(z,y) is integrable and
O f(z,y) is integrable over the rectangular region Rand S and T are subregions of Rsuch that R= SUT and
SnT ø exceptr an overlap on the boundaries, then Ør f(z,v)dA= [Ms (z,v)dA + [f, f(z,v)dA.
Of f(z,v) and g(z,y) are integrable over the rectangular region Rand f(z,y) > g(z,v) for (2, v) in R, then
fR z.v)dA > fn g(z,9)dA.
O(z,y) is integrable över the rectangular region Rand m < {(z,v) « M, then
mx A(R) < {f, f(z,v)dA < M x A(R).
0. Assume f(x,v) s integrable over the rectangular region R In the case where f(x,v) can be factored as a
product of a function g(z) of z only and a function h(y) of y only, then over the region
R (7.9)a < besy d), the double integral can be written as (z,y)dA (tz)dz) hujdy]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b7cc1c7-6b89-434c-9693-fee285d86a2f%2Fe4c8de20-1d62-406c-8c4c-a6f2bd291ba7%2F06gigb8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:DCICLL U C LUICLL OIISTCI UCIUW.
O If f(z.v) and g(z, v) are integrable over the rectangular region R, then the sum f(z,v) + g(z,v) is integrable and
ORz.9) + g(z,v)dA = OR f(z,v)dA + ffg9(z,v)dA
Of (z,y) is integrable over the rectangular region Rand c is a constant, then cf(z,y) is integrable and
O f(z,y) is integrable over the rectangular region Rand S and T are subregions of Rsuch that R= SUT and
SnT ø exceptr an overlap on the boundaries, then Ør f(z,v)dA= [Ms (z,v)dA + [f, f(z,v)dA.
Of f(z,v) and g(z,y) are integrable over the rectangular region Rand f(z,y) > g(z,v) for (2, v) in R, then
fR z.v)dA > fn g(z,9)dA.
O(z,y) is integrable över the rectangular region Rand m < {(z,v) « M, then
mx A(R) < {f, f(z,v)dA < M x A(R).
0. Assume f(x,v) s integrable over the rectangular region R In the case where f(x,v) can be factored as a
product of a function g(z) of z only and a function h(y) of y only, then over the region
R (7.9)a < besy d), the double integral can be written as (z,y)dA (tz)dz) hujdy]
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