For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. • f (x² - y²) dx + 2xydy; C' is the boundary of R = {(x,y): 0≤x≤1, 2x² ≤ y ≤ 2x} Jc 2.x²y dx + 2xydy; C is the boundary of R = {(x, y): 0≤x≤1, x² ≤ y ≤x} Jc 2ydx-3xd y; C is the circle x² + y² = 1 (e²² + y²) dx + (e¹² + x²)dy; C is the boundary of the triangle with vertices (0,0), (4,0) JC and (0,4) 3. 4.
For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. • f (x² - y²) dx + 2xydy; C' is the boundary of R = {(x,y): 0≤x≤1, 2x² ≤ y ≤ 2x} Jc 2.x²y dx + 2xydy; C is the boundary of R = {(x, y): 0≤x≤1, x² ≤ y ≤x} Jc 2ydx-3xd y; C is the circle x² + y² = 1 (e²² + y²) dx + (e¹² + x²)dy; C is the boundary of the triangle with vertices (0,0), (4,0) JC and (0,4) 3. 4.
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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For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve
C, traversed counterclockwise.
1.
f(x² - y²) dx + 2xydy; C is the boundary of R = {(x,y): 0≤x≤ 1, 2x² ≤ y ≤ 2x)
x³y dx + 2xydy; C is the boundary of R = {(x, y): 0 ≤x≤1, x² ≤ y ≤ x}
$²
2ydx-3xd y; C is the circle x² + y² = 1
2.
3.
4.
·f (ex² + y²) dx + (e¹² + x³)dy; C is the boundary of the triangle with vertices (0,0), (4,0)
and (0,4)
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