Mathematics, 11.06.2020 20:57 ericamoody14
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1), and back to the origin under the influence of the force field F(x, y, z) = z2i + 3xyj + 3y2k. Find the work done.
C
F · dr =
Answers: 1
.
and all four points are in the plane 
.
![\int_{C}^{}F.dx=\iint_{s}^{}curlF.dS\\\\=\iint_{D}^{}[-8y(0)-2z\left ( \frac{1}{4} \right )+5y]dA\\\\=\iint_{D}^{}\left ( -\frac{1}{2}z+5y \right )dA](/tpl/images/0683/1997/933c2.png)
![\int_{0}^{2}\left [ \frac{39}{16}y^2 \right ]_{0}^{4}dx\\\\=\int_{0}^{2}39\, \, dx\\\\=39\times 2\\\\=78 \, N](/tpl/images/0683/1997/08dde.png)
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A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1),...
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