Let f(x, y) lines x = = 3, x = y/2, and y = x in the xy-plane. (a) Express SÅ ƒ dA as a double integral in two different ways by filling in the values for the integrals below. (For one of these it will be necessary to write the double integral as a sum of two integrals, as indicated; for the other, it can be written as a single integral.) d x C = X b SR f dA = få fd f(x, y) dy where a = 0 = And SR f dA + Smf f(x,y) d where a = C = ²e and let R be the triangle bounded by th = .b So fd f(x, y) d x d " " b and d = n = d and q = = " = 3 | 2x , b = dy , m = p = (b) Evaluate one of your integrals to find the value of f f dA. SR f dA= "
Let f(x, y) lines x = = 3, x = y/2, and y = x in the xy-plane. (a) Express SÅ ƒ dA as a double integral in two different ways by filling in the values for the integrals below. (For one of these it will be necessary to write the double integral as a sum of two integrals, as indicated; for the other, it can be written as a single integral.) d x C = X b SR f dA = få fd f(x, y) dy where a = 0 = And SR f dA + Smf f(x,y) d where a = C = ²e and let R be the triangle bounded by th = .b So fd f(x, y) d x d " " b and d = n = d and q = = " = 3 | 2x , b = dy , m = p = (b) Evaluate one of your integrals to find the value of f f dA. SR f dA= "
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:lines x =
₁, Let f(x, y) = x² e² and let R be the triangle bounded by the
= 3, x = y/2, and y = x in the xy-plane.
R
(a) Express f f dA as a double integral in two different ways by filling
in the values for the integrals below. (For one of these it will be
necessary to write the double integral as a sum of two integrals, as
indicated; for the other, it can be written as a single integral.)
b
SR f dA = få få f(x, y) dy
where a = 0
C =
C =
X
d
And f₁ f dA = Så få f(x, y) d x
+ Sm S f (x, y) d
d
where a =
2
n =
and d = =
d =
"
and q =
d x
b=
=
b=
||
3
2x
dy
, m =
, p =
(b) Evaluate one of your integrals to find the value of f f dA.
SR fdA=
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