Let S be the plane with equation 2x +9y+z= 4 in the first octant and which...

  

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Let S be the plane with equation 2x +9y+z= 4 in the first octant and which is in front of the zy-plane. We wish to evaluate the surface integral JJ's 9x¹ds. The first step would be to parameterize the surface S. We will use the standard parameterization where z is a graph of z and y. y where (z,y) = D. Letr = x, y = y and z= We choose to express D as a Type 1 region. Then D = {(z,y)|0 ≤ ≤ ,0xy≤ Next, we calculate the partial derivatives of z with respect to a and y, respectively. 0: üz 82 By Finally, we can consider the surface integral: II, 9rds JJ, 9r¹ √GdA where G I+ z}. Let S be the plane with equation 2x +9y+z= 4 in the first octant and which is in front of the zy-plane. We wish to evaluate the surface integral JJ's 9x¹ds. The first step would be to parameterize the surface S. We will use the standard parameterization where z is a graph of z and y. y where (z,y) = D. Letr = x, y = y and z= We choose to express D as a Type 1 region. Then D = {(z,y)|0 ≤ ≤ ,0xy≤ Next, we calculate the partial derivatives of z with respect to a and y, respectively. 0: üz 82 By Finally, we can consider the surface integral: II, 9rds JJ, 9r¹ √GdA where G I+ z}.

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