Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.6, Problem 37PS
To determine
To find: The value of line integral using stokes theorem.
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1. Use Green's Theorem to evaluate
fo
(In x+y) dx-x² dy, where is the rectangle with vertices (1, 1),
(3, 1), (3, 4), (1, 4) oriented clockwise.
3. Evaluate the line integral (3ry² + 6y) dr, where C is the path traced by first moving from the
с
point (-3, 1) to the point (2, 1) along a straight line, then moving from the point (2, 1) to the
point (5,2) along the parabola x = = y² + 1.
Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (-3, 1), (-3, -2),
(2, –1), (2, 4), and back to (-3, 1), in that order. Use Green's theorem to evaluate the following integral.
(2xy) dx + (xy²) dy
Chapter 13 Solutions
Calculus
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- 1. Evaluate the integral [dx A S dx Ady + 3dx ^ dz of the 2-form w=dx^dy+3dx^dz over the oriented triangle S with vertices (0, 0, 0), (1,2,3), (1, 4, 0) in that order.arrow_forwardEvaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point P(1,–1, 2) to Q(3, 1, 2). 3.8arrow_forwardLet C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (−4, 2), (−4, −3), (2, −2), (2, 7), and back to (-4, 2), in that order. Use Green's theorem to evaluate the following integral. Jo (2xy) dx + (xy2) dyarrow_forward
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