Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the vectors (4, 5) and (5,3). (Give your answer in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) T(u, v) = (4u +5v,5u+ 3v) Calculate the double integral of e²x-y over P via change of variables. (Express numbers in exact form. Use symbolic notation and fractions where needed.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the vectors (4, 5) and (5,3).
(Give your answer in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.)
T(u, v) = (4u +5v,5u +3v)
Calculate the double integral of e²x-y over P via change of variables.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
1₂+²x-1
e²x- y dA =
-(²-1)(²-1)
Transcribed Image Text:Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the vectors (4, 5) and (5,3). (Give your answer in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) T(u, v) = (4u +5v,5u +3v) Calculate the double integral of e²x-y over P via change of variables. (Express numbers in exact form. Use symbolic notation and fractions where needed.) 1₂+²x-1 e²x- y dA = -(²-1)(²-1)
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