Calculus
Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Arc Length
Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic…
Line Integral
A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along…
Triple Integral
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Chapter 13.6, Problem 52PS
To determine

To find: The value of integral ∬S(curl F →⋅ N ^)dS by Stokes theorem.

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The vector function r(t) (5 – 2 sin t) i + (3+ 2 cos t) j + 2 k - traces out a circle in 3-space as t varies. In which plane does this circle lie? 1. plane x 2. plane y 2 3. plane z = -2 4. plane z = 2 5. plane x = -2 6. plane y = -2
Let F = . LF C Use Stokes' Theorem to evaluate dr, where C is the triangle with vertices (7,0,0), (0,7,0), and (0,0,7), oriented counterclockwise as viewed from above.
Let F = . Use Stokes' Theorem to evaluate curlF · dS , where S consists of the top and the four sides (but not the bottom) of the cube with one corner at (-3,-3,-3) and the diagonal corner at (1,1,1). Hint: Use the fact that if S1 and S2 share the same boundary curve C that curlF · dS F· dī = curlF · d§

Chapter 13 Solutions

Calculus

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