Let D1 be the region in the XY-plane enclosed by the triangle with vertices (0, 0),(1, 1),(2, 0). Let D2 be the semi-circular region of radius 1 with the center at (1, 0) lying below the x-axis. Let D = D1 U D2. a) Argue whether D is an elementary region. b) Compute the area of D. c) Without using Green's theorem, evaluate c(xydx + x?dy), where C denotes the boundary of D oriented clockwise. d) Use Green's theorem to evaluate the line integral given in part c).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let D1 be the region in the XY-plane enclosed
by the triangle with vertices (0, 0),(1, 1).(2, 0).
Let D2 be the semi-circular region of radius 1
with the center at (1, 0) lying below the x-axis.
Let D = D1 U D2.
a) Argue whether D is an elementary region.
b) Compute the area of D.
c) Without using Green's theorem, evaluate f
c(xydx + x²dy), where C denotes the boundary
of D oriented clockwise.
d) Use Green's theorem to evaluate the line
integral given in part c).
Transcribed Image Text:Let D1 be the region in the XY-plane enclosed by the triangle with vertices (0, 0),(1, 1).(2, 0). Let D2 be the semi-circular region of radius 1 with the center at (1, 0) lying below the x-axis. Let D = D1 U D2. a) Argue whether D is an elementary region. b) Compute the area of D. c) Without using Green's theorem, evaluate f c(xydx + x²dy), where C denotes the boundary of D oriented clockwise. d) Use Green's theorem to evaluate the line integral given in part c).
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