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Compute the following integral using the Green's identity. In(x² + y² + 1) A ((x² + y² + 1)²) dx dy, where D := {(x,y) : x² + y² < 1}. (Hint: for any point (x, y) on the boundary JD of D, the outward unit normal direction (x, y) = (x, y)).

Compute the following integral using the Green's identity. In(x² + y² + 1) A ((x² + y² + 1)²) dx dy, where D := {(x,y) : x² + y² < 1}. (Hint: for any point (x, y) on the boundary JD of D, the outward unit normal direction (x, y) = (x, y)).

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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3. Compute the following integral using the Green's identity. √In(x² + y² + 1)A ((x² + y² + 1)²) dx dy, where D := {(x,y): x² + y² < 1}. (Hint: for any point (x, y) on the boundary ID of D, the outward unit normal direction ñ(x, y) = (x, y)).
Transcribed Image Text:3. Compute the following integral using the Green's identity. √In(x² + y² + 1)A ((x² + y² + 1)²) dx dy, where D := {(x,y): x² + y² < 1}. (Hint: for any point (x, y) on the boundary ID of D, the outward unit normal direction ñ(x, y) = (x, y)).
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