Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.6, Problem 30PS
To determine
To find: The value of given
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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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- Consider I = ∫CF⋅dr, where (img17) is a conservative vector field and curve C is parameterized by:α (t): = ((2 − cos (5t)) cost, (2 − cos (5t)) synt, sin (5t)) with 0≤t≤π. We have that the value of I is equal to: (img18)arrow_forwardConsider the vector field F=(x^2+y^2,10xy). Compute the line integrals ∫c_1 F⋅dr and ∫c_2 F⋅dr, where c_1 (t)=(t, t^2) and c_2 (t)=(t, t) for 0≤t≤1. Can you decide from your answers whether or not F is a gradient vector field? Why or why not?arrow_forward5.Find the circulation of the field F(x, y, z) = (x-y)i+2yj around the circler(t) = costi+ sin tj , 0<=t<=2πarrow_forward
- In the given problem (section a), we used the parameterizationr(t) = ⟨cos t, sin t, 3 cos2 t + sin2 t⟩ for C. Confirm that theparameterization C: r(t) = ⟨cos t, sin t, 4 - cos2 t - 3 sin2 t⟩ alsoresults in an answer of 2π. Using Stokes’ Theorem to evaluate a surface integral Evaluate∫∫S (∇ x F) # n dS, where F = -y i + x j + z k, in the following cases.a. S is the part of the paraboloid z = 4 - x2 - 3y2 that lies within the paraboloid z = 3x2 + y2 (the blue surface as shown). Assume n pointsin the upward direction on S.b. S is the part of the paraboloid z = 3x2 + y2 that lies within the paraboloidz = 4 - x2 - 3y2, with n pointing in the upward direction on S.c. S is the surface in part (b), but n pointing in the downward direction on S.arrow_forwardWhat is the total differential: w = (x^2)(z^2) + sin(yz)arrow_forwardProblem 8. Determine whether the field F is conservative. If it is, evaluate (integral) F · dr where C is the plane curve with equation r(t) = [cos(t), sin (t)]-π/2≤ t ≤π/2F(x, y) = (sin x + cos y)i + (2 − x sin y)j.arrow_forward
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