Let F(r, y) = (-y, x² +1) be a vector field and R the region of the plane bounded by the triangle with vertices (-1,0), (1,0), (0, 2). 1. Find the line integral of F along the boundary of the region R. 2. Obtain the same result by using Green's Theorem (which amounts to calculating a double integral).

Let F(r, y) = (-y, x² +1) be a vector field and R the region of the plane bounded by the triangle with vertices (-1,0), (1,0), (0, 2). 1. Find the line integral of F along the boundary of the region R. 2. Obtain the same result by using Green's Theorem (which amounts to calculating a double integral).

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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Question

Let F(x, y) = (-y, x² +1) be a vector field and R the region of the plane bounded by the
triangle with vertices (-1,0), (1,0), (0, 2).
%3D
1. Find the line integral of F along the boundary of the region R.
2. Obtain the same result by using Green's Theorem (which amounts to calculating a
double integral).

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