Express the line integral in terms of t 2ry dr + 4x²y dy = 1, 2zy dz + 4z'y dy + 2ry dr + 4x?y dy + 2ry dr + 4x?y dy Σ dt + Σ dt + E dt. where a = Σ Evaluate the integral 2ry dr + 4x²y dy = Σ Now using Green's Theorem express 2xy dr + 4x*y dy as a double integral $ 2ry dz + 4x²y dy = ΣdA Given the shape of the region of integration, how should we evaluate the above integral? OA. Rectangular Coordinates: dy dr OB. Polar Coordinates: dr de OC. None of the above M M
Express the line integral in terms of t 2ry dr + 4x²y dy = 1, 2zy dz + 4z'y dy + 2ry dr + 4x?y dy + 2ry dr + 4x?y dy Σ dt + Σ dt + E dt. where a = Σ Evaluate the integral 2ry dr + 4x²y dy = Σ Now using Green's Theorem express 2xy dr + 4x*y dy as a double integral $ 2ry dz + 4x²y dy = ΣdA Given the shape of the region of integration, how should we evaluate the above integral? OA. Rectangular Coordinates: dy dr OB. Polar Coordinates: dr de OC. None of the above M M
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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Transcribed Image Text:Evaluate the line integral by following the given steps.
2xy dx + 4x?y dy
C is the triangle with vertices (0, 0),(3,0), and (0, 5).
The curve C can split up into each one of its sides (shown in the picture below)
H(t)
L(t)
B(t)
$ 2ry dr + 4x?y dy
2xy dx + 4x?y dy +
2ry dx + 4x?y dy +
2ry da + 4x?y dy
Parametrize each side of the triangle
B(t)
<3t.0>
Σ
te
Σ
Σ
H(t) = <3-3t, t>
Σ
te
Σ
1
Σ
L(t) = <0,1-t>
Σ
te
Σ.
Σ
(use the most natural parametrizations and remember which direction you need to go)
Express the line integral in terms of t
2ay dx + 4x?y dy
2ry dx + 4x?y dy +
2xy dx + 4x?y dy +
2xy dx + 4x?y dy
Σ dt +
E dt +
Σdt .
Transcribed Image Text:Express the line integral in terms of t
2ry dx + 4x?y dy
2xy dæ + 4x°y dy + :
2xy da + 4a?y dy + /
2xy dr + 4x²y dy
Σ dt +
Σ dt +
E dt.
where
a =
Σ
b =
Σ
Evaluate the integral
2xy dx + 4x?y dy =
Σ
Now using Green's Theorem express
2xy da + 4x²y dy as a double integral
2xy dr + 4x?y dy =
ΣdA
Given the shape of the region of integration, how should we evaluate the above integral?
OA. Rectangular Coordinates: dy dx
OB. Polar Coordinates: dr de
OC. None of the above
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