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, Problem 48SP
To determine
To evaluate: The surface integral
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1. Please
20. Let S be an oriented surface parametrized by r(u,v). Define the
notation do = r, du × r, dv so that do is a vector normal to
the surface. Also, the magnitude do =
face area (by Equation 5 in Section 16.5). Derive the identity
do is the element of sur-
do = (EG – F²)'/² du dv
where
E = r?, F = r„ • r,,
and G = |r,|?.
Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N
is a vector normal to the surface S. Determine F as well as the area of the plane perpendicular
to F if surface S = 2xy + 3z.
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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