Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi + (5 - 3x)j+ (z² – 2)k across the surface S defined as T(6,0) = (/3 sin o cos 0)i + (/3 sin o sin 0)j + (V3 cos o)k, where 0<0

Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F= 3yi + (5 - 3x)j+ (z² – 2)k across the surface S defined as T(6,0) = (/3 sin o cos 0)i + (/3 sin o sin 0)j + (V3 cos o)k, where 0<0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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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 path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length.

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 a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.

Triple Integral

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Question

Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field
F- 3yi + (5 – 3x)j+(z² – 2)k across the surface S defined as
F(6,0) = (/3 sin o cos 0)i + (v3 sin ø sin 0) j + (/3 cos o)k, where
0<0 <T/2, 0 so< 2m
in the direction away from the origin.
OS
(Just write the result, do not write any intermediate calculational steps, use "pi for Tif
needed.)

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