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Carry out the affine transformation | u = (x + y)/V2 lv= (y - x)/V2 in the improper double integral dxdy 1- xy 3(2) = where S is the unit square [0, 1) × [0, 1), in order to show that 1/v t dt 3(2) = 4 arctan V2 – 1² V2- 1² dt +4 arctan 2 – 12 V2- 12 V2 cos 20 in the above integrals respec- Then substitutet = \2 sin 0 and t = tively.

Carry out the affine transformation | u = (x + y)/V2 lv= (y - x)/V2 in the improper double integral dxdy 1- xy 3(2) = where S is the unit square [0, 1) × [0, 1), in order to show that 1/v t dt 3(2) = 4 arctan V2 – 1² V2- 1² dt +4 arctan 2 – 12 V2- 12 V2 cos 20 in the above integrals respec- Then substitutet = \2 sin 0 and t = tively.

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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Carry out the affine transformation 1= (x + y)/V2 v = (y – x)/V2 in the improper double integral dxdy 1- ху 3(2) = where S is the unit square [0, 1) × [0, 1), in order to show that •1/V2 dt t Š(2) = 4 0, arctan V2 - 12 V2- 12 V2 - t dt + 4 arctan V2-12 V2-12 2 – 2 – 12 Then substitute t = \2 sin 0 and t = \2 cos 20 in the above integrals respec- %3D tively.
Transcribed Image Text:Carry out the affine transformation 1= (x + y)/V2 v = (y – x)/V2 in the improper double integral dxdy 1- ху 3(2) = where S is the unit square [0, 1) × [0, 1), in order to show that •1/V2 dt t Š(2) = 4 0, arctan V2 - 12 V2- 12 V2 - t dt + 4 arctan V2-12 V2-12 2 – 2 – 12 Then substitute t = \2 sin 0 and t = \2 cos 20 in the above integrals respec- %3D tively.
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