Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.4, Problem 1PS
To determine
To find: The line integral using the Green’s theorem around the closed curve C. Check the result using parameterization.
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24. Show that Legendre's equation
(1-x²)y" - 2xy - λy=0
is self-adjoint.
Let C be the curve represented by the equations
10t, y = t², (0 ≤ t ≤ 1). In each part, evaluate
the line integral along C.
x =
NOTE: Enter the exact answers.
(a) √(x - √y)ds
= 2.25
X
(b)
√(x - √ỹ)dx = [45
[
(c) √(x - √y)dy = [6
Suppose
5
F(x, y) = 8 sin () sin ()7 - 8 cos (2) cos (2) ³
2
2
and C is the curve from P to Qin the figure. Calculate the
line integral of along the curve C.
The labeled points are P = (– ³7, ³7),
Q = (– ³T, − ³ ), R = (³, ³), and S = ( ³7, — ³″ ).
The curves PR and SQ are trigonometric functions of
period 2π and amplitude 1.
La
F. dr =
-5
(Click on graph to enlarge)
4
5
Chapter 13 Solutions
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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Prob. 60CRP
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