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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
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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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
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]
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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