Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
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.
.2
Evaluate the line integral xy dx + x-dy, where C is the path going
counterclockwise around the boundary of the rectangle with corners (0,0),(2,0),(2,3),
and (0,3). You can evaluate directly or use Green's theorem. Write the integral(s), but
do not evaluate.
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Chapter 13 Solutions
Student's Solution and Survival Manual for Calculus
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- 5. Prove that the equation has no solution in an ordered integral domain.arrow_forwardLet 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) dyarrow_forwardВ. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .arrow_forward
- 4) Evaluate the integral (2e-2x) dy + (2xy +1) dx using Green's theorem where C is C 64 consists of y =4-x² and straight line from (-2,0) to (2,0). Sketch the curve C. ans: 3arrow_forwardProblem. Use Green's Theorem, So ӘР dA, ду Рах + Qdy дх to evaluate the line integral, (–x² + e" In y)dx + (x+ y² + et dy, where C is the triangle with the vertices (1, 1), (2, 1), and (2, 2), and the positive (counter- clockwise) orientation.arrow_forward35. Evaluate F.dr: (a) F = (x+z)i +zj+yk. C is the line from (2,4,4) to (1,5,2). (b) F= x²i+zsin(yz)j + y sin(yz)k. C is the curve from A4(0,0,1) to B(3,1,2) as shown below. B A (c) F = yi-xj+zk. C is the circle of radius 3 centered on the z-axis in the plane z=4 oriented clockwise when viewed from above. (d) F = 4x³i + (x+y)j. C is the curve y=sin(2x) from (0,0) to (7/2,0). (e) F = (-y³ + sin(x²))ī + (x³ − ln(y² +1)) j . C is the circle of radius 5 centered at (0,0) in the .xy- plane oriented counterclockwise.arrow_forward
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