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- Part 2 Express your double integrals in terms of r and 0. (4г — 5у) da + (5х + 3у) dy 3D -4sintcost+20 Σ dr dθ where ri = 0 Σ r2 = Σ 0, = 0 Σ 02 = Σ M M MM

- Part 2 Express your double integrals in terms of r and 0. (4г — 5у) da + (5х + 3у) dy 3D -4sintcost+20 Σ dr dθ where ri = 0 Σ r2 = Σ 0, = 0 Σ 02 = Σ M M MM

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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- Part 2 Express your double integrals in terms of r and 0. 02 (4x – 5y) dæ + (5x + 3y) dy = | | Σ dr dθ -4sintcost+20 where r2 = Σ 01 = Σ 02 = Σ M M M M
Transcribed Image Text:- Part 2 Express your double integrals in terms of r and 0. 02 (4x – 5y) dæ + (5x + 3y) dy = | | Σ dr dθ -4sintcost+20 where r2 = Σ 01 = Σ 02 = Σ M M M M
- Part 1 Evaluate the line integral by following the given steps. $ (4x – 5y) da + (5x + 3y) dy C is the circle x² + y? = 4 The curve C can be parametrized by r(t) = <2cost, 2sint> Σ te Σ 2pi (use the most natural parametrization) Express the line integral in terms of t (4х — 5у) dx + (5х + 3у) dy — -4sintcost+20 Σ dt. where a = 6 = 2pi Σ Evaluate the integral ф (4т — 5у) dx + (5x + 3у) dy %3D 40pі Σ Now using Green's Theorem express (4x – 5y) dx +(5x + 3y) dy as a double integral (4x – 5y) dx + (5x + 3y) dy= 10 Σ dA Given the shape of the region of integration, how should we evaluate the above integral? OA. Rectangular Coordinates: dy dx O B. Polar Coordinates: dr d0 OC. None of the above M M
Transcribed Image Text:- Part 1 Evaluate the line integral by following the given steps. $ (4x – 5y) da + (5x + 3y) dy C is the circle x² + y? = 4 The curve C can be parametrized by r(t) = <2cost, 2sint> Σ te Σ 2pi (use the most natural parametrization) Express the line integral in terms of t (4х — 5у) dx + (5х + 3у) dy — -4sintcost+20 Σ dt. where a = 6 = 2pi Σ Evaluate the integral ф (4т — 5у) dx + (5x + 3у) dy %3D 40pі Σ Now using Green's Theorem express (4x – 5y) dx +(5x + 3y) dy as a double integral (4x – 5y) dx + (5x + 3y) dy= 10 Σ dA Given the shape of the region of integration, how should we evaluate the above integral? OA. Rectangular Coordinates: dy dx O B. Polar Coordinates: dr d0 OC. None of the above M M
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