Concept explainers
Area of a region in a plane Let R be a region in a plane that has a unit normal
a. Show that ▿ × F = n
b. Use Stokes’ Theorem to show that
c. Consider the curve C given by r = 〈5 sin t, 13 cos t, 12 sin t〉, for 0 ≤ t ≤ 2p. Prove that C lies in a plane by showing that
d. Use part (b) to find the area of the region enclosed by C in part (c). (Hint: Find the unit normal vector that is consistent with the orientation of C.)
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Calculus: Early Transcendentals (3rd Edition)
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