Mathematics, 24.08.2020 01:01 mary9664
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
Answers: 2
![$ = 27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2t+27 [ - \cos^3 t]_0^{2 \pi}$](/tpl/images/0728/0190/675f5.png)
![$= \frac{2187}{8}[t-\frac{1}{4} \sin 4t]_0^{2 \pi} $](/tpl/images/0728/0190/f65b3.png)
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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part...
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