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Calc III Ch15 Notes_Part27

Calc III Ch15 Notes_Part27 - 15.8 — Stoke’s Theorem‘...

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Unformatted text preview: 15.8 — Stoke’s Theorem‘ Stoke’s Theorem gives the relationship between a surface integral over an oriented surface and a line integral along a closed space curve which forms the boundary of the surface. NOTE: We call the orientation positive if it follows the I’lgfh’f’ — HAND WM Theorem: Ex: Let S be an oriented surface with unit normal vector N, bounded by a piecewise smooth simple closed curve C. If F is a vector field whose component functions have continuous partials on a an Open region containing S and C, then LF- dr= f/(ZW/F) W45 Use Stoke’ 5 Thm to calculate LF- dr where F(x,y,z)= (x+y )i+(y-i~z2 )j+(z+x )k -deis the triangle formed? by (1. 0, 0). (0,1,0). and (01 0, 1)- ...
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