Evaluate the integral [] exp(-5x² − 2xy − 5y² + x)dxdy R2

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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How to evaluate this integral via completing the square? We worked on a similar problem (also attached)

Evaluate the integral
[] exp(-5x² – 2xy − 5y² + x)dxdy
Transcribed Image Text:Evaluate the integral [] exp(-5x² – 2xy − 5y² + x)dxdy
1/SS₁² exp(-x² - xy-3x² + x) dudy
- Complete the square (scalar form, matrix reclar form)
:Pdf of N (10²)
qualifiers pdf
L2T² exe (-
क
(x-4)²
20²
S000 Sooo exp(-x² - XY - 3y² + x dr
integrate urt X (y; constant)
A
500 5000 exp (-x² _x(4-1) - (₁²², (²-²²-3₁ ²² dxdy
(y-1), (x-1
4
Y-1
(+-1)2²³
B
Y-1→>>
Se exe (C=22² -34³) 500 ep (-(x + 1¹23²5²) dedy
Exp
4
eb
A
-mathe translation
• 5000 exe ((1-23²-3x³) (5000 exe (-2²) dt) dv
4
-t=x+1=1
·dt=dx
8
5000 exp (²74² - 3y²) dy * 500 exp (t²) dt
x
Se 12no² exp(-x_^)^²) dx = 1
•S000 exp(-x²) dx - 5²00
20²
-2
5250
•Sep (1²2) at 0²³-¹/12 M=0, (t-o)²
ex
→
2
چن
2₂
Transcribed Image Text:1/SS₁² exp(-x² - xy-3x² + x) dudy - Complete the square (scalar form, matrix reclar form) :Pdf of N (10²) qualifiers pdf L2T² exe (- क (x-4)² 20² S000 Sooo exp(-x² - XY - 3y² + x dr integrate urt X (y; constant) A 500 5000 exp (-x² _x(4-1) - (₁²², (²-²²-3₁ ²² dxdy (y-1), (x-1 4 Y-1 (+-1)2²³ B Y-1→>> Se exe (C=22² -34³) 500 ep (-(x + 1¹23²5²) dedy Exp 4 eb A -mathe translation • 5000 exe ((1-23²-3x³) (5000 exe (-2²) dt) dv 4 -t=x+1=1 ·dt=dx 8 5000 exp (²74² - 3y²) dy * 500 exp (t²) dt x Se 12no² exp(-x_^)^²) dx = 1 •S000 exp(-x²) dx - 5²00 20² -2 5250 •Sep (1²2) at 0²³-¹/12 M=0, (t-o)² ex → 2 چن 2₂
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