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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
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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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: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 .
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
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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