Evaluate the integral by making an appropriate change of variables. 5(x + y) cos (x² - y²) dA, where R is the rectangle enclosed by the lines x - y = 0, x- y = 10, x + y = 0, and x+y = 8 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with respect to u,v? ANSWER: 5(x + y) cos (x2 – y?) dA = [cos (81) – 80] O cos (80) + 81] O Icos (81) + 1)] O-[cos (81) + 80] O-cos (80) – 1] O (cos (80) – 81]
Evaluate the integral by making an appropriate change of variables. 5(x + y) cos (x² - y²) dA, where R is the rectangle enclosed by the lines x - y = 0, x- y = 10, x + y = 0, and x+y = 8 Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped to R in the xy-plane; what is the Jacobian of x,y with respect to u,v? ANSWER: 5(x + y) cos (x2 – y?) dA = [cos (81) – 80] O cos (80) + 81] O Icos (81) + 1)] O-[cos (81) + 80] O-cos (80) – 1] O (cos (80) – 81]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 74E
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![Evaluate the integral by making an appropriate change of variables.
5(x + y) cos (x² - y2) dA, where R is the rectangle enclosed by the lines x- y = 0, x-y = 10,
x + y = 0, and x +y = 8
Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped
to R in the xy-plane; what is the Jacobian of x,y with respect to u,v?
ANSWER:
5(x + y) cos (x² - y2) dA =
O [cos (81) – 80]
O (cos (80) + 81]
O Icos (81) + 1)]
-[cos (81) + 80]
(cos (80) - 1]
O (cos (80) - 81]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F718b1378-40e4-4c32-83bc-211fc46d7de4%2F795f0be0-6d33-4b27-acd9-ea599d3e9f2d%2Fi4xpl7c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate the integral by making an appropriate change of variables.
5(x + y) cos (x² - y2) dA, where R is the rectangle enclosed by the lines x- y = 0, x-y = 10,
x + y = 0, and x +y = 8
Hints: If we set u = x-y, v=x+y, how are x and y expressed in terms of u and v; which region D in the uv-plane is mapped
to R in the xy-plane; what is the Jacobian of x,y with respect to u,v?
ANSWER:
5(x + y) cos (x² - y2) dA =
O [cos (81) – 80]
O (cos (80) + 81]
O Icos (81) + 1)]
-[cos (81) + 80]
(cos (80) - 1]
O (cos (80) - 81]
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