Mathematics, 07.12.2019 01:31 zanaplen27
Evaluate the integral of the function f(x, y, z) = x + y over the surface s given by the following. φ(u, v) = (2u cos(v), 2u sin(v), u), u is in [0, 7], v is in [0, π]
Answers: 1
![\bf \displaystyle\iint_Rf(\phi(u,v))\left\|\displaystyle\frac{\partial \phi}{\partial u}\times\displaystyle\frac{\partial\phi}{\partial v}\right\|dudv=\displaystyle\int_{0}^{7}\displaystyle\int_{0}^{\pi}[(2u cos(v)+2u sin(v))2\sqrt{u^2+4}]dudv=\\\\=2\displaystyle\int_{0}^{7}u\sqrt{u^2+4}du\left(\displaystyle\int_{0}^{\pi}cos(v)dv+\displaystyle\int_{0}^{\pi}sin(v)dv\right)=](/tpl/images/0407/3200/570c0.png)
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Evaluate the integral of the function f(x, y, z) = x + y over the surface s given by the following....
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